<PAGE>

                                                                    Exhibit 4.11

                         FIRST AMENDMENT AND SUPPLEMENT
                               TO CREDIT AGREEMENT

                             Dated November 6, 2001,
                     to be effective as of November 16, 2001

                                      among

                       ENTERPRISE PRODUCTS OPERATING L.P.

                            The Lenders Party Hereto

                           FIRST UNION NATIONAL BANK,
                             as Administrative Agent

                   BANK ONE, N.A. and THE BANK OF NOVA SCOTIA,
                            as Co-Syndication Agents

                             FLEET NATIONAL BANK and
             WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW YORK BRANCH,
                           as Co-Documentation Agents

               ------------------------------------------------

                          FIRST UNION SECURITIES, INC.,
                     As Sole Arranger and Sole Book Manager

                        364-Day Revolving Credit Facility
<PAGE>

                         FIRST AMENDMENT AND SUPPLEMENT
                         ------------------------------
                               TO CREDIT AGREEMENT
                               -------------------

     THIS FIRST AMENDMENT AND SUPPLEMENT TO CREDIT AGREEMENT (this "First
                                                                    -----
Amendment") is made and entered into this 6th day of November, 2001, to be
---------
effective as of the 16th day of November of 2001 (the "Effective Date"), among
                                                       --------------
ENTERPRISE PRODUCTS OPERATING L.P., a Delaware limited partnership ("Borrower");
                                                                     --------
FIRST UNION NATIONAL BANK, as administrative agent (in such capacity, the
"Administrative Agent") for each of the lenders (the "Lenders") that is a
 --------------------                                 -------
signatory or which becomes a signatory to the hereinafter defined Credit
Agreement; and the Lenders.

                                R E C I T A L S:
                                - - - - - - - -

     A. On November 17, 2000, the Borrower, the Lenders and the Administrative
Agent entered into a certain Credit Agreement (the "Credit Agreement") whereby,
                                                    ----------------
upon the terms and conditions therein stated, the Lenders agreed to make certain
Loans (as such term is defined in the Credit Agreement) and extend certain
credit to the Borrower.

     B. Bank One, N.A. and The Bank of Nova Scotia have been appointed to act as
Co-Syndication Agents under the Credit Agreement from and after the Effective
Date of this First Amendment; and Fleet National Bank and Westdeutsche
Landesbank Girozentrale, New York Branch have been appointed to act as
Co-Documentation Agents under the Credit Agreement from and after the Effective
Date of this First Amendment.

     C. First Union Securities, Inc. shall be the Sole Arranger and Sole Book
Manager under the Credit Agreement from and after the Effective Date of this
First Amendment.

     D. In view of the foregoing, the Borrower, the Lenders and the
Administrative Agent mutually desire to amend certain aspects of the Credit
Agreement to, among other things, (i) extend the Availability Period for three
hundred sixty-four (364) days, and (ii) reflect the changes in the Arranger,
Book Manager, Syndication Agent and Documentation Agent.

     NOW, THEREFORE, in consideration of the mutual covenants and agreements
herein contained, the Borrower, the Lenders and the Administrative Agent hereby
agree that the Credit Agreement shall be amended as follows:

     1. Certain Definitions.

          1.1 Terms Defined Above. As used in this First Amendment, the terms
              -------------------
"Administrative Agent", "Borrower", "Credit Agreement", "Effective Date" and
"First Amendment", shall have the meanings indicated above.

                                       -1-
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          1.2 Terms Defined in Agreement. Unless otherwise defined herein, all
              --------------------------
terms beginning with a capital letter which are defined in the Credit Agreement
shall have the same meanings herein as therein unless the context hereof
otherwise requires.

     2. Amendments to Credit Agreement.

          2.1 Defined Terms. The following terms defined in Section 1.02 of the
              -------------
Credit Agreement are hereby amended as follows:

               (a) The term "Agreement" is hereby amended to mean the Credit
Agreement, as amended and supplemented by this First Amendment and as the same
may from time to time be further amended or supplemented.

               (b) The term "Conversion" is hereby amended in its entirety to
read as follows:

                    "`Conversion' means the conversion of the outstanding
                      ----------
               Revolving Loans to Term Loans pursuant to the terms and
               conditions of Section 2.01(d), which conversion shall occur on
               November 15, 2002, unless the Availability Period is extended
               pursuant to Section 2.01(c)."

          2.2 Additional Defined Term. Section 1.02 of the Credit Agreement is
              -----------------------
hereby further amended and supplemented by adding the following new definition,
which reads in its entirety as follows:

          "'First Amendment' shall mean that certain First Amendment and
            ---------------
     Supplement to Credit Agreement dated November 6, 2001, to be effective as
     of November 16, 2001, among the Borrower, the Lenders and the
     Administrative Agent."

          2.3 Schedule 2.01 - Commitments. Schedule 2.01 attached to the Credit
              ---------------------------
Agreement is hereby replaced and superseded by Schedule 2.01 attached to this
First Amendment. From and after the Effective Date of this First Amendment, each
Lender's Commitment shall be as set forth on Schedule 2.01 attached to this
First Amendment.

     3. Conditions Precedent. In addition to all other applicable conditions
        -------------------
precedent contained in the Credit Agreement, the obligation of the Lenders and
the Administrative Agent to enter into this First Amendment shall be conditioned
upon the following conditions precedent:

          (a) The Administrative Agent shall have received a copy of this First
Amendment, duly completed and executed by the Borrower;

          (b) The Administrative Agent shall have received such other
information, documents or instruments as it or its counsel may reasonably
request.

                                       -2-
<PAGE>

     4. Default. Any default under this First Amendment shall constitute a
        -------
default under the Credit Agreement.

     5. Representations and Warranties. The Borrower represents and warrants to
        ------------------------------
the Lenders and the Administrative Agent that:

          (a) there exists no Default or Event of Default, or any condition or
act which constitutes, or with notice or lapse of time or both would constitute,
an Event of Default under the Credit Agreement, as hereby amended and
supplemented;

          (b) the Borrower has performed and complied with all covenants,
agreements and conditions contained in the Credit Agreement, as hereby amended
and supplemented, required to be performed or complied with by it; and

          (c) the representations and warranties of the Borrower contained in
the Credit Agreement, as hereby amended and supplemented, were true and correct
when made, and are true and correct in all material respects at and as of the
time of delivery of this First Amendment.

     6. Extent of Amendments. Except as expressly herein set forth, all of the
        --------------------
terms, conditions, defined terms, covenants, representations, warranties and all
other provisions of the Credit Agreement are herein ratified and confirmed and
shall remain in full force and effect.

     7. Counterparts. This First Amendment may be executed in two or more
        ------------
counterparts, and it shall not be necessary that the signatures of all parties
hereto be contained on any one counterpart hereof; each counterpart shall be
deemed an original, but all of which together shall constitute one and same
instrument.

     8. References. On and after the Effective Date hereof, the terms
        ----------
"Agreement", "hereof", "herein", "hereunder", and terms of like import when used
in the Credit Agreement shall, except where the context otherwise requires,
refer to the Credit Agreement, as amended and supplemented by this First
Amendment.

     THIS FIRST AMENDMENT, THE CREDIT AGREEMENT, AS AMENDED HEREBY, THE NOTES
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.

     This First Amendment shall benefit and bind the parties hereto, as well as
their respective assigns, successors, heirs and legal representatives.

                                       -3-
<PAGE>

     EXECUTED this 6/th/ day of November, 2001, effective as of the Effective
Date.

                   BORROWER:
                   ---------

                   ENTERPRISE PRODUCTS OPERATING L.P.


                   By: Enterprise Products GP, LLC, General Partner


                       By:     /s/ W. Randall Fowler
                               -----------------------------------
                       Name:    W. Randall Fowler
                       Title:   Vice President and Treasurer


                   LENDERS AND AGENTS:
                   ------------------

                   FIRST UNION NATIONAL BANK,
                   Individually and as Administrative Agent


                   By:      /s/ Russell Clingman
                            --------------------------------------
                   Name:    Russell Clingman
                   Title:   Vice President

                   BANK ONE, NA (Main Office - Chicago),
                   Individually and as Co-Syndication Agent


                   By:      /s/ Kenneth J. Fatur
                            --------------------------------------
                   Name:    Kenneth J. Fatur
                   Title:   Director, Capital Markets

                   THE BANK OF NOVA SCOTIA,  Individually  and as
                   Co-Syndication Agent


                   By:      /s/ N. Bell
                            --------------------------------------
                   Name:    N. Bell
                   Title:   Assistant Agent

                   THE FUJI BANK, LIMITED, Individually and as
                   Managing Agent


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

                                      -4-
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                   FLEET  NATIONAL  BANK,  Individually  and as
                   Co-Documentation Agent


                   By:      /s/ Christopher C. Holmgren
                            --------------------------------------
                   Name:    Christopher C. Holmgren
                   Title:   Managing Director

                   WESTDEUTSCHE LANDESBANK
                   GIRONZENTRALE,  NEW   YORK   BRANCH,
                   Individually and as Co-Documentation Agent


                   By:      /s/ Jeffrey S. Davidson    /s/ Paul Verdi
                            -----------------------------------------
                   Name:    Jeffrey S. Davidson        Paul Verdi
                   Title:   Associate Director         Manager

                   TORONTO DOMINION (TEXAS), INC.


                   By:      /s/ Carolyn R. Faeth
                            --------------------------------------
                   Name:    Carolyn R. Faeth
                   Title:   Vice President

                   GUARANTY BANK


                   By:      /s/ Jim R. Hamilton
                            --------------------------------------
                   Name:    James R. Hamilton
                   Title:   Senior Vice President

                   HIBERNIA NATIONAL BANK


                   By:      /s/ Nancy G. Moragas
                            --------------------------------------
                   Name:    Nancy G. Moragas
                   Title:   Vice President

                   THE DAI-ICHI KANGYO BANK, LIMITED
                   Individually and as Managing Agent


                   By:      /s/ Perzemek T. Blaziak
                            --------------------------------------
                   Name:    Perzemek T. Blaziak
                   Title:   Account Officer

                                      -5-
<PAGE>

                   BANK OF TOKYO-MITSUBISHI, LTD., HOUSTON AGENCY


                   By:      /s/ K. Glasscock
                            --------------------------------------
                   Name:    K. Glasscock
                   Title:   VP & Manager

                   SUNTRUST BANK,
                   Individually and as Managing Agent


                   By:      /s/ David J. Edge
                            --------------------------------------
                   Name:    David J. Edge
                   Title:   Director

                   CITIBANK, N.A.


                   By:      /s/ Dougalas A. Whiddon
                       -------------------------------------------
                   Name:    Dougalas A. Whiddon
                   Title:   Attorney-In-Fact

                                      -6-
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                                  SCHEDULE 2.01

                                   COMMITMENTS
                                   -----------

              Lender                                          Commitment
              -------                                         ----------
      First Union National Bank                              $15,875,000

      Bank One, NA (Main Office - Chicago)                   $15,000,000

      Toronto Dominion (Texas), Inc.                         $12,500,000

      Fleet National Bank                                    $15,000,000

      The Fuji Bank, Limited                                 $9,750,000

      The Dai-Ichi Kangyo Bank, Limited                      $5,250,000

      Bank of Tokyo - Mitsubishi, Ltd.,                      $10,000,000
      Houston Agency

      SunTrust Bank                                          $13,500,000

      Westdeutsche Landesbank Girozentrale,                  $15,000,000
      New York Branch

      Guaranty Bank                                          $7,500,000

      Citibank NA                                            $10,000,000

      The Bank of Nova Scotia                                $15,000,000

      Hibernia National Bank                                 $5,625,000

                                      -7-