<PAGE>

                                                                    EXHIBIT 10.2

                                FIRST AMENDMENT
                              TO CREDIT AGREEMENT
                      (364-Day Revolving Credit Facility)


          THIS FIRST AMENDMENT TO CREDIT AGREEMENT dated as of February 28, 2001
(the "First Amendment"), among PURE RESOURCES, INC., a Delaware corporation (the
      ---------------
"Borrower"), the lenders party hereto (the "Lenders"), and THE CHASE MANHATTAN
 --------                                   -------
BANK, individually, as Issuing Bank and as Administrative Agent (the
"Administrative Agent").
 --------------------

                             W I T N E S S E T H:
                             -------------------

          WHEREAS, the Borrower, the Lenders, and the Administrative Agent are
parties to that certain Credit Agreement dated as of September 29, 2000 (the
"Credit Agreement"), whereby, pursuant to the terms and conditions contained
 ----------------
therein, the Lenders agreed to make loans to and extensions on behalf of the
Borrower under a $250,000,000 364-day revolving credit facility; and

          WHEREAS, the parties to the Credit Agreement intend to amend the
Credit Agreement to add additional Lenders as parties to the Credit Agreement
pursuant to Section 2.01(c)(ii) thereof and to otherwise amend the Credit
Agreement;

          NOW, THEREFORE, the parties to the Credit Agreement hereby agree as
follows:

          SECTION 1.  Amendments to Credit Agreement.
                      ------------------------------

          (a)  Section 1.01 of the Credit Agreement hereby is amended by
inserting the following definitions in their appropriate alphabetical order:

               "Agreement" means this Credit Agreement dated as of September 29,
     2000, among the Borrower, the Lenders, the Administrative Agent and the
     Issuing Bank, as amended by the First Amendment, and as the same may be
     further amended, waived or otherwise modified from time to time in
     accordance herewith.

               "First Amendment" means that certain First Amendment to Credit
                ---------------
     Agreement dated as of February 28, 2001, among the Borrower, the Lenders
     party thereto, the Administrative Agent and the Issuing Bank.

          (b)  The definition of "Lenders" appearing in Section 1.01 of the
                                                        ------------
Credit Agreement hereby is amended in its entirety to read as follows:

               "Lenders" means the lenders listed on Schedule 2.01 attached to
                -------                              -------------
     the First Amendment, and any other Person that shall have become a party to
     this Agreement pursuant to an Assignment and Acceptance, other than any
     such

                                       1
<PAGE>

     Person that ceases to be a party hereto pursuant to an Assignment and
     Acceptance."

          (c)  Schedule 2.01 attached to the Credit Agreement is hereby amended
               -------------
and restated by replacing Schedule 2.01 attached to the Credit Agreement in its
                          -------------
entirety with Schedule 2.01 attached to this First Amendment.  From and after
              -------------
the date of this First Amendment, all references contained in the Credit
Agreement to Schedule 2.01 shall be references to Schedule 2.01 attached to this
             -------------                        -------------
First Amendment.

          SECTION 2. Conditions Precedent to Effectiveness.  This First
                     -------------------------------------
Amendment shall become effective as of the date hereof when the Administrative
Agent shall have received:

          (a)  counterparts hereof duly executed by the Borrower, the Lenders,
the Administrative Agent and the Issuing Bank (or, in the case of any party as
to which an executed counterpart shall not have been received, telegraphic,
telex, or other written confirmation from such party of execution of a
counterpart hereof by such party);

          (b)  to the extent requested by any of the Lenders signatory to this
First Amendment, duly executed Notes payable to the order of such Lender
reflecting such Lender's Commitment as set forth on Schedule 2.01 attached
                                                    -------------
hereto; and

          (c)  no  Default or Event of Default shall have occurred and be
continuing as of the date of this First Amendment.

Upon effectiveness of this First Amendment, each Lender signatory to this First
Amendment shall for all purposes be a Lender party to the Credit Agreement, as
amended by this First Amendment, and any other Loan Documents executed by the
Lenders and shall have the rights and obligations of a Lender under the Loan
Documents to the same extent as if they were originally parties to the Credit
Agreement, and no further consent or action by the Borrower, the Lenders, the
Administrative Agent or the Issuing Bank shall be required and the Lenders shall
have the Commitments set forth in Schedule 2.01 attached hereto.
                                  -------------

          SECTION 3. Reaffirmation of Representations and Warranties.  To
                     -----------------------------------------------
induce the Lenders, the Administrative Agent and the Issuing Bank to enter into
this First Amendment, the Borrower hereby reaffirms, as of the date hereof, its
representations and warranties in their entirety contained in Article III of the
                                                              -----------
Credit Agreement and in all other documents executed pursuant thereto (except to
the extent such representations and warranties relate solely to an earlier date)
and additionally represents and warrants as follows:

          (a)  The Borrower is a corporation duly organized, validly existing
and in good standing under the laws of its jurisdiction of formation and has all
power and authority and all governmental licenses, authorizations, consents and
approvals required in each case to carry on its business, except to the extent
that the failure to have such power, authority, licenses, authorizations,
consents and approvals could not reasonably be expected to have a Material
Adverse Effect.

          (b)  The execution, delivery and performance by the Borrower of this
First Amendment are within the Borrower's corporate powers, have been duly
authorized by all

                                       2
<PAGE>

necessary corporate action of the Borrower, require, in respect of the Borrower,
no action by or in respect of, or filing with, any governmental body, agency or
official and do not contravene or constitute a default under, any provision of
law or regulation (including Regulation X issued by the Federal Reserve Board)
applicable to the Borrower or Regulation U or the articles or certificate of
incorporation of the Borrower or the bylaws of the Borrower or any judgment,
injunction, order, decree or material agreement binding upon the Borrower or
result in or require the creation or imposition of any Lien on any asset of the
Borrower.

          (c)  This First Amendment has been duly executed and delivered by the
Borrower.  This First Amendment, the Credit Agreement, as amended by this First
Amendment, and each other Loan Document to which the Borrower is a party are
legal, valid and binding obligations of the Borrower enforceable against the
Borrower in accordance with their respective terms, except as the enforceability
thereof may be limited by any applicable bankruptcy, insolvency, reorganization,
moratorium or similar laws affecting creditors' rights generally and by general
principles of equity.

          (d)  Since September 29, 2000, no event or circumstance has occurred
that has resulted in or could reasonably be expected to have a Material Adverse
Effect.  No Event of Default has occurred and is continuing as of the date
hereof.

          (e)  There is no action, suit or proceeding pending against the
Borrower, or to the knowledge of the Borrower threatened against the Borrower,
before any court or arbitrator or any governmental body, agency or official in
which there is a reasonable possibility of an adverse decision which could
reasonably be expected to have a Material Adverse Effect or which in any manner
draws into question the legality, validity, binding effect or enforceability of
this First Amendment, the Credit Agreement, as amended hereby, or any other Loan
Document.

          SECTION 4. Defined Terms.  Except as amended hereby, terms used herein
                     -------------
when defined in the Credit Agreement shall have the same meanings herein unless
the context otherwise requires.

          SECTION 5. Reaffirmation of Credit Agreement.  This First Amendment
                     ---------------------------------
shall be deemed to be an amendment to the Credit Agreement, and the Credit
Agreement, as amended hereby, is hereby ratified, approved and confirmed in each
and every respect. All references to the Credit Agreement herein and in any
other document, instrument, agreement or writing shall hereafter be deemed to
refer to the Credit Agreement as amended hereby.

          SECTION 6. Governing Law; Entire Agreement.  This First Amendment and
                     -------------------------------
the Notes shall be governed by, and construed in accordance with, the laws of
the State of Texas. The Credit Agreement as amended by this First Amendment, the
Notes and the other Loan Documents constitute the entire understanding among the
parties hereto with respect to the subject matter hereof and supersede any prior
agreements, written or oral, with respect thereto.

          SECTION 7. Severability of Provisions.  Any provision in this First
                     --------------------------
Amendment that is held to be inoperative, unenforceable, or invalid in any
jurisdiction shall, as to that jurisdiction, be inoperative, unenforceable, or
invalid without affecting the remaining provisions

                                       3
<PAGE>

in that jurisdiction or the operation, enforceability, or validity of that
provision in any other jurisdiction, and to this end the provisions of this
First Amendment are declared to be severable.

          SECTION 8.  Counterparts.  This First Amendment may be executed in any
                      ------------
number of counterparts, all of which taken together shall constitute one
agreement, and any of the parties hereto may execute this First Amendment by
signing any such counterpart.

          SECTION 9.  Headings.  Article and section headings in this First
                      --------
Amendment are for convenience of reference only, and shall not govern the
interpretation of any of the provisions of this First Amendment.

          SECTION 10. Successors and Assigns.  This First Amendment shall be
                      ------------
binding upon and inure to the benefit of the parties hereto and their respective
successors and assigns.


                     [SIGNATURES BEGIN ON FOLLOWING PAGE]

                                       4
<PAGE>

          IN WITNESS WHEREOF, the Borrower, the Lenders, the Administrative
Agent, the Syndication Agent, the Documentation Agent and the Issuing Bank have
executed this First Amendment as of the date first above written.


                              PURE RESOURCES, INC.


                              By: /s/ William K. White
                                  -------------------------------
                              Name:   William K. White
                              Title:  Vice President



           [First Amendment to Credit Agreement - Signature Page 1]

                                       5
<PAGE>

                              THE CHASE MANHATTAN BANK, individually
                              and as Administrative Agent,


                              By: /s/ Robert Traband
                                 ----------------------------------
                              Name:   Robert Traband
                              Title:  Vice President

                              Lending Office for ABR Loans and
                              Eurodollar Loans and Address for Notice:

                              The Chase Manhattan Bank
                              One Chase Manhattan Plaza, 8th Floor
                              New York, New York 10081

                              Telecopier No. 212/552-2261
                              Attention: Muniram Appanna



           [First Amendment to Credit Agreement - Signature Page 2]

                                       6
<PAGE>

                              FIRST UNION NATIONAL BANK, individually
                              and as Syndication Agent


                              By:     /s/ Robert R. Weteroff
                                 ------------------------------------
                              Name:   Robert R. Weteroff
                              Title:  Senior Vice President

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              301 South College Street
                              Charlotte, North Carolina 28288

                              Address for Notice:

                              Business/Credit:
                              First Union National Bank
                              1001 Fannin Street, Suite 2255
                              Houston, Texas 77002
                              Telephone No.: 713/346-2717
                              Telecopier No.: 713/650-6354
                              Attention: David E. Humphreys

                              Administrative:
                              First Union National Bank
                              1001 Fannin Street, Suite 2255
                              Houston, Texas 77002
                              Telephone No.: 713/346-2727
                              Telecopier No.: 713/650-6354
                              Attention: Debbie Blank



           [First Amendment to Credit Agreement - Signature Page 3]

                                       7
<PAGE>

                              THE BANK OF NEW YORK


                              By:     /s/ Peter Keller
                                 ----------------------------------
                              Name:   Peter Keller
                              Title:  Vice President


                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              The Bank of New York
                              101 Barclay Street
                              New York, New York 10286
                              Attn: Bill Barbiero

                              Address for Notice:\

                              Business/Credit:
                              The Bank of New York
                              One Wall Street, 19th Floor
                              New York, New York 10286
                              Telephone No.: 212/635-7861
                              Telecopier No.: 212/635-7923
                              Attn.: Peter Keller

                              Administrative:

                              The Bank of New York
                              One Wall Street, 19th Floor
                              New York, New York 10286
                              Telephone No.: 212/635-7532
                              Telecopier No.: 212/635-7923
                              Attn.: Theresa M. Burk



           [First Amendment to Credit Agreement - Signature Page 4]

                                       8
<PAGE>

                              CREDIT LYONNAIS NEW YORK BRANCH


                              By:________________________________
                              Name:
                              Title:

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              Credit Lyonnais New York Branch
                              1301 Avenue of the Americas
                              New York, New York 10019

                              Address for Notice:

                              Business/Credit:
                              Credit Lyonnais
                              1000 Louisiana, Suite 5360
                              Houston, Texas 77002
                              Telephone No.: 713/753-8713
                              Telecopier No.: 713/751-0307
                              Attention: John Grandstaff

                              Administrative:
                              Credit Lyonnais New York Branch
                              1301Avenue of the Americas
                              New York, New York 10019
                              Telephone No.: 212/261-7633
                              Telecopier No.: 917/849-5440
                              Attention: Bindu Menon



           [First Amendment to Credit Agreement - Signature Page 5]

                                       9
<PAGE>

                              BNP PARIBAS, individually and as Documentation
                              Agent


                              By:___________________________________________
                              Name:
                              Title:

                              By:___________________________________________
                              Name:
                              Title:

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              BNP Paribas
                              1200 Smith Street, Suite 3100
                              Houston, Texas 77002

                              Address for Notice:

                              Business/Credit:
                              1200 Smith Street, Suite 3100
                              Houston, Texas 77002
                              Telephone No.: 713/659-4811
                              Telecopier No.: 713/659-6915
                              Attention: Brian Malone

                              Administrative:
                              1200 Smith Street, Suite 3100
                              Houston, Texas 77002
                              Telephone No.: 713/982-1126
                              Telecopier No.: 713/659-5305
                              Attention: Leah Evans Hughes



           [First Amendment to Credit Agreement - Signature Page 6]

                                      10
<PAGE>

                              BANK ONE, TEXAS, N.A.


                              By"___________________________________
                              Name:
                              Title:

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              Bank One, Texas, N.A.
                              1717 Main Street, 4th Floor
                              Dallas, Texas 75201

                              Address for Notice:

                              Business/Credit:
                              1717 Main Street, 4th Floor
                              Dallas, Texas 75201
                              Telephone No.: 214/290-2212
                              Telecopier No.: 214/290-2332
                              Attention: Mark Cranmer

                              Administrative:
                              1717 Main Street, 3rd Floor
                              Dallas, Texas 75201
                              Telephone No.: 214/290-2652
                              Telecopier No.: 214/290-2627
                              Attention: Nancy Daniel



           [First Amendment to Credit Agreement - Signature Page 7]

                                      11
<PAGE>

                              THE FUJI BANK, LIMITED

                              By:     /s/ Jacques Azagury
                                  --------------------------------------------
                              Name:   Jacques Azagury
                              Title:  Senior Vice President & Manager

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              The Fuji Bank, Limited
                              Two World Trade Center
                              New York, New York 70048

                              Address for Notice:

                              Business Credit:
                              The Fuji Bank, Limited
                              One Houston Center
                              1221 McKinney Street, Suite 4100
                              Houston, Texas 77010
                              Telephone No.: 713/759-1800
                              Telecopier No.: 713/759-0717
                              Attention: Mark Polasek

                              Administrative:
                              The Fuji Bank, Limited
                              Two World Trade Center
                              New York, New York 70048
                              Telephone No.: 212/898-2099
                              Telecopier No.: 212/488-8216
                              Attention: Tina Catapano



           [First Amendment to Credit Agreement - Signature Page 8]

                                      12
<PAGE>

                              CIBC, INC.


                              By:     /s/ Nora Q. Catiis
                                 -----------------------------------------
                              Name:   Nora Q. Catiis
                              Title:  Authorized Signatory

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              CIBC, Inc.
                              2 Paces West
                              2727 Paces Ferry Road, Suite 1200
                              Attention: Tanya Hunter

                              Address for Notice:

                              Business/Credit:
                              CIBC World Markets
                              1600 Smith Street, Suite 3100
                              Houston, Texas 77002
                              Telephone No.: 713/650-2588
                              Telecopier No.: 713/650-7675
                              Attention: Mack Wolf

                              Administrative:
                              CIBC, Inc.
                              2 Paces West
                              2727 Paces Ferry Road, Suite 1200
                              Atlanta, Georgia 30339
                              Telephone No.: 770/319-4828
                              Telecopier No.: 770/319-4950
                              Attention: Anita Rounds



           [First Amendment to Credit Agreement - Signature Page 9]

                                      13
<PAGE>

                              WELLS FARGO BANK (TEXAS), N.A.


                              By:_____________________________________
                              Name:
                              Title:

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              Wells Fargo Bank Texas, N.A.
                              1445 Ross Avenue, Suite 200,
                              MAC T 5303 - 029
                              Dallas, Texas 75202

                              Address for Notice:

                              Business/Credit:
                              Wells Fargo Bank Texas, N.A.
                              1445 Ross Avenue, Suite 200,
                              MAC T 5303 - 029
                              Dallas, Texas 75202
                              Telephone No.: 214/777-4026
                              Telecopier No.: 214/303-1839
                              Attention: Charles D.  Kirkham

                              Administrative:
                              Wells Fargo Bank, N.A.
                              1740 Broadway
                              Denver, Colorado 80274
                              Telephone No.: 303/863-6102
                              Telecopier No.: 303/863-2729
                              Attention: Tanya Ivie



           [First Amendment to Credit Agreement - Signature Page 10]

                                      14
<PAGE>

                              FLEET NATIONAL BANK


                              By:     /s/ Stephen J. Hoffman
                                 -------------------------------------------
                              Name:   Stephen J. Hoffman
                              Title:  Vice President

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              Fleet National Bank
                              100 Federal Street
                              M/C: MADE10008A
                              Boston, Massachusetts 02211

                              Address for Notice:

                              Business/Credit:
                              Fleet National Bank
                              100 Federal Street
                              M/C: MADE10008A
                              Boston, Massachusetts 02211
                              Telephone No.: 617/434-8849
                              Telecopier No.: 617/434-3652
                              Attention: Stephen Hoffman

                              Administrative:
                              Fleet National Bank
                              One Federal Street
                              M/C: MADE1008A
                              Boston, Massachusetts 02211
                              Telephone No.: 617/434-5092
                              Telecopier No.: 617/434-0201
                              Attention: Francia Castillo



           [First Amendment to Credit Agreement - Signature Page 11]

                                      15
<PAGE>

                              THE SANWA BANK LIMITED


                              By:     /s/ Ryoichi Konishi
                                 -------------------------------------
                              Name:   Ryoichi Konishi
                              Title:  Assistant Vice President


                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              The Sanwa Bank Limited
                              55 East 52nd Street
                              New York, NY 10055

                              Address for Notice:

                              C. Lawrence Murphy
                              55 East 52nd Street
                              New York, NY 10055

                              Administrative:
                              Priscilla Mark
                              55 East 52nd Street
                              New York, NY 10055



           [First Amendment to Credit Agreement - Signature Page 12]

                                      16
<PAGE>

                              THE BANK OF TOKYO-MITSUBISHI, LTD.


                              By:     /s/ Kelton Glasscock
                                 -----------------------------------------
                              Name:   Kelton Glasscock
                              Title:  Vice President

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              The Bank of Tokyo-Mitsubishi, Ltd.
                              1100 Louisiana Street, Suite 2800
                              Houston, TX  77002
                              Telecopier No.:  713/658-0116
                              Attention: ________

                              Business/Credit:
                              1100 Louisiana Street, Suite 2800
                              Houston, TX  77002
                              Telecopier No.:  713/658-0116
                              Attention: John Stanton

                              Administrative:
                              1100 Louisiana Street, Suite 2800
                              Houston, TX  77002
                              Telecopier No.:  713/658-0116
                              Attention: Nadra Breir



           [First Amendment to Credit Agreement - Signature Page 13]

                                      17
<PAGE>

                              CREDIT SUISSE FIRST BOSTON


                              By:     /s/ Bill O'Daly
                                 ------------------------------------
                              Name:   Bill O'Daly
                              Title:  Vice President

                              Lending Office for ABR Loans and
                              Eurodollar Loans:

                              Credit Suisse First Boston
                              11 Madison Avenue
                              New York, New York 10010
                              Telecopier No.:  212/325-8615

                              Business/Credit:
                              11 Madison Avenue
                              New York, New York 10010-3629
                              Telecopier No.:  212/325-8615
                              Attention:  James Moran

                              Administrative:
                              5 World Trade Center
                              New York, New York 10048
                              Telecopier No.:  212/335-0593
                              Attention:  Christina Maurillo



           [First Amendment to Credit Agreement - Signature Page 14]

                                      18
<PAGE>

                                                                   SCHEDULE 2.01

                                  COMMITMENTS

<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------------
               Lender                                Commitment            Percentage Share
               ------                                ----------            ----------------
<S>                                                 <C>                    <C>
----------------------------------------------------------------------------------------------
    The Chase Manhattan Bank                        $ 25,000,000           10.638297872%
----------------------------------------------------------------------------------------------
    First Union National Bank                       $ 25,000,000           10.638297872%
----------------------------------------------------------------------------------------------
          BNP Paribas                               $ 25,000,000           10.638297872%
----------------------------------------------------------------------------------------------
  Credit Lyonnais New York Branch                   $ 25,000,000           10.638297872%
----------------------------------------------------------------------------------------------
       Bank One, Texas, N.A.                        $ 25,000,000           10.638297872%
----------------------------------------------------------------------------------------------
        Fleet National Bank                         $ 22,500,000            9.574468085%
----------------------------------------------------------------------------------------------
       The Bank of New York                         $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
           CIBC, Inc.                               $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
       The Fuji Bank, Limited                       $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
   Wells Fargo Bank Texas, N.A.                     $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
           Sanwa Bank                               $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
 The Bank of Tokyo-Mitsuibishi, Ltd.                $ 12,500,000            5.319148936%
----------------------------------------------------------------------------------------------
      Credit Suisse First Boston                    $ 12,500,000            5.319148936%
                                                    ------------            -----------
----------------------------------------------------------------------------------------------
                     Total:                         $235,000,000          100.000000000%
----------------------------------------------------------------------------------------------
</TABLE>


                            [Schedule 2.01 - Page 1]

                                      19