<PAGE>

                                                                  EXHIBIT 10.4.1


                               FIRST AMENDMENT TO
                  SECOND AMENDED AND RESTATED CREDIT AGREEMENT


                         dated as of September 30, 2000


                                     among


                     SPINNAKER EXPLORATION COMPANY, L.L.C.,
                                  AS BORROWER

                                      and

                        CERTAIN FINANCIAL INSTITUTIONS,
                                  AS LENDERS,

                        TORONTO DOMINION (TEXAS), INC.,
                            AS ADMINISTRATIVE AGENT,

                                      and

                          CREDIT SUISSE FIRST BOSTON,
                             AS DOCUMENTATION AGENT
<PAGE>

                               FIRST AMENDMENT TO
                  SECOND AMENDED AND RESTATED CREDIT AGREEMENT

     THIS FIRST AMENDMENT TO SECOND AMENDED AND RESTATED CREDIT AGREEMENT, dated
as of September 30, 2000 (this "First Amendment"), is among SPINNAKER
EXPLORATION COMPANY, L.L.C., a Delaware limited liability company (the
"Borrower"), the commercial lending institutions parties hereto (the "Lenders"),
CREDIT SUISSE FIRST BOSTON, as documentation agent (in such capacity, the
"Documentation Agent") for the Lenders, and TORONTO DOMINION (TEXAS), INC., as
administrative agent (in such capacity together with its successors in such
capacity, the "Administrative Agent") for the Lenders.

                              W I T N E S S E T H:

     WHEREAS, Borrower, the Administrative Agent, the Documentation Agent, the
Issuer and the Lenders have heretofore entered into that certain Second Amended
and Restated Credit Agreement, dated as of July 20, 2000 (as may be amended,
supplemented, restated or otherwise modified from time to time, the "Credit
Agreement"); and

     WHEREAS, Borrower, the Administrative Agent, the Documentation Agent, the
Issuer and the Lenders now intend to amend the Credit Agreement in certain
respects.

     NOW, THEREFORE, in consideration of the premises and of the mutual
covenants herein contained, each of Borrower, the Administrative Agent, the
Issuer and the Lenders agree as follows:

     SECTION 1.  Defined Terms.  Terms defined in the Credit Agreement
are used in this First Amendment with the same meaning, unless otherwise
indicated.

     SECTION 2.  Amendments to Credit Agreement.

     A.   Section 1.1 of the Credit Agreement is hereby amended by adding the
following definition in appropriate alphabetical order:

          ""Mark to Market Exposure" means the net amount, from time to time,
     that would be required to terminate all outstanding transactions then open
     under Hedging Agreements between the Borrower and any other Person."

     B.   Section 6.2(f)(i) of the Credit Agreement is hereby amended and
restated in its entirety as follows:

          "(i)  Permitted Investments and investments permitted by Section
     6.2(g);"

     C.   Section 6.2(k) of the Credit Agreement is hereby amended and restated
in its entirety as follows:
<PAGE>

          "(k)  Current Ratio.  The ratio of Borrower's consolidated current
     assets (excluding Mark to Market Exposure) as of the end of each Fiscal
     Quarter to Borrower's consolidated current liabilities (excluding Mark to
     Market Exposure) as of the end of such Fiscal Quarter will never be less
     than 1.00 to 1.00.  For purposes of this subsection, Borrower's
     consolidated current ratio will be calculated (i) including availability
     under this Agreement as current assets, and (ii) excluding as current
     liabilities any payments of principal on the Notes which are required to be
     repaid within one year from the time of calculation."

     D.   Section 6.2(n)(i) of the Credit Agreement is hereby amended by
replacing the words "one hundred percent (100%)" with the words "eighty percent
(80%)".

     E.   Section 6.2(n)(iii) of the Credit Agreement is hereby amended and
restated in its entirety as follows:

          "(iii)  at no time will any Hedging Agreement of any nature (including
     any such contracts described in clauses (i) and (ii) above) have a
     counterparty with a minimum long-term senior unsecured Indebtedness rating
     less than "BBB" by Standard & Poors Corporation or "Baa" by Moody's
     Investors Services, Inc."

     SECTION 3.   Conditions to Effectiveness.  The effectiveness of this
First Amendment shall be subject to the prior or concurrent satisfaction, on or
before September 30, 2000, of the conditions precedent that the Administrative
Agent shall have received all of the following, in form and substance
satisfactory to the Administrative Agent, and in sufficient number of signed
counterparts to provide one for each Lender:

     A.   Counterparts of this First Amendment, duly executed by each of
Borrower, the Administrative Agent, the Documentation Agent, the Issuer and the
Majority Lenders; and

     B.   Such other documents as the Administrative Agent may reasonably
request.

     Upon satisfaction of the foregoing conditions precedent, this First
Amendment shall be effective as of the date first above written.

     SECTION 4.   Representations and Warranties.  To induce the Lenders,
the Issuer, the Administrative Agent and the Documentation Agent to enter into
this First Amendment, Borrower hereby reaffirms, as of the date hereof, its
representations and warranties contained in Article V of the Credit Agreement
(except to the extent such representations and warranties relate solely to an
earlier date, in which case such representations and warranties shall relate
solely to such earlier date) and additionally represents and warrants as
follows:

     A.   Authorization.  Borrower has duly taken all action necessary to
authorize the execution and delivery by it of this First Amendment and to
authorize the consummation of the transactions contemplated thereby and the
performance of its obligations hereunder.

                                       2
<PAGE>

     B.   No Conflicts or Consents.  The execution and delivery by Borrower of
this First Amendment, the performance by each of its obligations under this
First Amendment, and the consummation of the transactions contemplated by this
First Amendment, do not and will not (i) conflict with any provision of (1) any
domestic or foreign law, statute, rule or regulation, (2) the organizational
documents of Borrower, or (3) any agreement, judgment, license, order or permit
applicable to or binding upon Borrower, (ii) result in the acceleration of any
Indebtedness owed by Borrower, or (iii) result in or require the creation of any
Lien upon any assets or properties of Borrower except as expressly contemplated
in the Loan Documents.  Except as expressly contemplated in the Loan Documents,
no consent, approval, authorization or order of, and no notice to or filing with
any court or Governmental Authority or third party is required in connection
with the execution, delivery or performance by Borrower of this First Amendment
or to consummate any transactions contemplated by this First Amendment.

     C.   Enforceable Obligations.  This First Amendment and the Credit
Agreement as amended by this First Amendment will, on the due execution and
delivery hereof, constitute the legal, valid and binding obligations of
Borrower, enforceable in accordance with their terms except as such enforcement
may be limited by bankruptcy, insolvency or similar laws of general application
relating to the enforcement of creditors' rights and subject to general
principles of equity, regardless of whether considered in a proceeding in equity
or at law.

     D.   No Defaults.  No Default has occurred and is continuing.

     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 in any other
document, instrument, agreement or writing shall hereafter be deemed to refer to
the Credit Agreement as amended hereby.

     SECTION 6.   Severability.  If any term or provision of any First
Amendment shall be determined to be illegal or unenforceable all other terms and
provisions of this First Amendment shall nevertheless remain effective and shall
be enforced to the fullest extent permitted by applicable law.

     SECTION 7.   Headings.  The various headings of this First Amendment
are inserted for convenience only and shall not affect the meaning or
interpretation of this First Amendment or any provisions hereof or thereof.

     SECTION 8.   Counterparts. This First Amendment may be separately
executed in any number of counterparts and by different parties hereto in
separate counterparts, each of which when so executed shall be deemed to
constitute one and the same agreement.

     SECTION 9.   GOVERNING LAW.  THIS FIRST AMENDMENT SHALL BE DEEMED
CONTRACTS AND INSTRUMENTS MADE UNDER THE LAWS OF THE STATE OF TEXAS AND SHALL BE
CONSTRUED AND ENFORCED IN ACCORDANCE

                                       3
<PAGE>

WITH AND GOVERNED BY THE LAWS OF THE STATE OF TEXAS AND THE LAWS OF THE UNITED
STATES OF AMERICA.

     SECTION 10.  Successors and Assigns.  The provisions of this First
Amendment shall be binding upon and inure to the benefit of the parties hereto
and their respective successor and assigns, except that Borrower may not assign
or otherwise transfer any of its rights under this First Amendment without the
prior written consent of all Lenders.

     SECTION 11.  ENTIRE AGREEMENT.  THIS WRITTEN FIRST AMENDMENT AND THE
OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY
NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES.

     THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

                            [SIGNATURE PAGES FOLLOW]

                                       4
<PAGE>

        IN WITNESS WHEREOF, the parties hereto have caused this First Amendment
to be duly executed by their respective officers as of the day and year first
above written.


                             SPINNAKER EXPLORATION COMPANY, L.L.C.


                             By:   SPINNAKER EXPLORATION COMPANY,
                                     as Managing Member


                             By:  /s/ JAMES M. ALEXANDER
                                ----------------------------
                             Name:  James M. Alexander
                             Title: VP, CFO, Secretary


                             TORONTO DOMINION (TEXAS), INC.,
                             as Administrative Agent and as a Lender


                             By: /s/ JANO MOTT
                                ----------------------------
                             Name: Jano Mott
                             Title: Vice President


                             CREDIT SUISSE FIRST BOSTON,
                             as Documentation Agent and as a Lender


                             By: /s/ JAMES P. MORAN
                                ----------------------------
                             Name: James P. Moran
                             Title: Director


                             By: /s/ DAVID W. KRATOVIL
                                ----------------------------
                             Name: David W. Kratovil
                             Title: Director

                                      S-1
<PAGE>

                             THE TORONTO-DOMINION BANK,
                             as Issuer


                             By:    /s/ JANO MOTT
                                ----------------------------
                             Name:  Jano Mott
                             Title: Manager, Syndication &
                                    Credit Administration

                                      S-2