<PAGE>

                                                                     EXHIBIT 4.6

                     FOURTH AMENDMENT TO RIGHTS AGREEMENT

          FOURTH AMENDMENT (this "Fourth Amendment to Rights Agreement"), dated
as of September 6, 2001 to the Rights Agreement between Sun Company, Inc. and
First Chicago Trust Company of New York, as Rights Agent dated as of February 1,
1996, as amended July 3, 1997, February 3, 2000, and July 6, 2001 (the "Rights
Agreement").

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

          A.   Pursuant to Section 27 of the Rights Agreement, Sunoco, Inc., the
successor by name change to Sun Company, Inc. (the "Company") and Equiserve
Trust Company, NA, the successor to First Chicago Trust Company of New York (the
"Rights Agent"), shall, if the Company so directs, supplement or amend any
provision of the Rights Agreement in accordance with the provisions of Section
27 thereof.

          B.   The Board of Directors has declared it advisable and in the best
interests of the Company and its stockholders to amend the Rights Agreement in
the manner set forth below.

                               A G R E E M E N T
                               -----------------

          NOW, THEREFORE, in consideration of the foregoing and the covenants
set forth herein, the Company hereby directs, and the parties hereto agree that,
the Rights Agreement is amended as follows:

     1.   The definition of "Acquiring Person" set forth in Section 1 of the
Rights Agreement is amended and supplemented to add the following sentence to
the end of such definition:

     Notwithstanding the foregoing, if the Board of Directors of the Company
     determines in good faith that a person who would otherwise be an "Acquiring
     Person," as defined pursuant to the foregoing provisions of this paragraph,
     has become such inadvertently, and such Person divests as promptly as
     practicable a sufficient number of shares of Voting Stock so that such
     Person would no longer be an "Acquiring Person," as defined pursuant to the
     foregoing provisions of this paragraph, then such Person shall not be
     deemed to be an "Acquiring Person" for any purposes of this Agreement.

     2.   Section 11(a)(i)(D) and Section 11(c) of the Rights Agreement are each
amended to replace the phrase "consolidation or merger" with the phrase
"consolidation, merger, share exchange or division".

     3.   Section 11(n) of the Rights Agreement is amended to read in its
entirety as follows:

          (n)  The Company covenants and agrees that it will not at any time
     after the Distribution Date (i) consolidate, merge, engage in a share
     exchange or otherwise combine with, (ii) divide or (iii) sell or otherwise
     transfer, (and/or permit any of its Subsidiaries to sell or

                                      -1-
<PAGE>

     otherwise transfer), in one transaction or a series of related
     transactions, assets or earning power aggregating more than 50% of the
     assets or earning power of the Company and its Subsidiaries taken as a
     whole, to any other Person or Persons if (x) at the time of or immediately
     after such consolidation, merger, share exchange, combination, division or
     sale there are any rights, warrants or other instruments or securities
     outstanding or any agreements or arrangements in effect which would
     substantially diminish or otherwise eliminate the benefits intended to be
     afforded by the Rights or (y) prior to, simultaneously with or immediately
     after such consolidation, merger, share exchange, combination, division or
     sale, the stockholders of a Person who constitutes, or would constitute,
     the "Principal Party" for the purposes of Section 13 shall have received a
     distribution of Rights previously owned by such Person or any of its
     Affiliates and Associates.

     4.   Section 13(a)(x) of the Rights Agreement is amended to read in its
entirety as follows:

          (x) the Company shall consolidate with, merge into, or otherwise
     combine with, any other Person, or the Company shall divide into two or
     more corporations and the Company shall not be the continuing or surviving
     corporation of such consolidation, merger, combination or division.

     5.   Section 13(a)(y) of the Rights Agreement is amended to read in its
entirety as follows:

          (y) any Person shall merge into, or otherwise combine with, the
     Company, or the Company shall divide into two or more corporations, and the
     Company shall be the continuing or surviving corporation of such merger,
     combination or division, or the Company shall engage in a share exchange,
     and, in connection with the merger, combination, division or share
     exchange, all or part of the outstanding shares of the Common Stock shall
     be changed into or exchanged for other stock or securities of the Company
     or any other Person, cash or any other property, or

     6.   Section 13(a)(1)(B), Section 13(a)(2) and Section 13(c) of the Rights
Agreement are each amended to replace the phrase "consolidation, merger,
combination, sale or transfer" with the phrase "consolidation, merger,
combination, share exchange, division, sale or transfer."

     7.   Section 13(b)(i) of the Rights Agreement is amended to replace the
phrase "merger, consolidation or combination" in each place that it appears with
the phrase  "consolidation, merger, combination, share exchange or division."

     8.   Section 23(a) of the Rights Agreement is amended to read in its
entirety as follows:

     (a) The Board of Directors of the Company may, at its option, at any time
     prior to the earlier of (i) such time as any Person becomes an Acquiring
     Person, and (ii) the Final Expiration Date, redeem all but not less than
     all of the then outstanding Rights at a redemption price of $.01 per Right,
     as such amount may be appropriately adjusted to reflect any stock split,
     stock dividend or similar transaction

                                      -2-
<PAGE>

     occurring after the date hereof (such redemption price being hereinafter
     referred to as the "Redemption Price"); provided, however, that if the
                                             --------  -------
     Board of Directors of the Company authorizes redemption of the Rights in
     the following circumstance, then there must be Continuing Directors in
     office and such authorization shall require the concurrence of a majority
     of the Continuing Directors: such authorization occurs on or within ninety
     (90) days of the date of a change (resulting from a proxy or consent
     solicitation or a series of solicitations) in a majority of the directors
     of the Company in office at the commencement of such solicitation (or
     series of solicitations) if any Person who is a participant in such
     solicitation has stated (or if upon the commencement of such solicitation,
     a majority of the directors of the Company has determined in good faith)
     that such Person (or any of its Affiliates or Associates) intends to take,
     or may consider taking, any action which would result in such Person
     becoming an Acquiring Person or which would cause the occurrence of a
     Triggering Event.

     9.   Section 25(a) of the Rights Agreement is amended:  (a) to replace the
phrase "consolidation or merger" in each place that it appears with the phrase
"consolidation, merger or share exchange"; (b) to replace the phrase "to effect
the liquidation, dissolution or winding up of the Company" with the phrase "to
effect a division or the liquidation, dissolution or winding up of the Company";
and (c) to replace the phrase "reclassification, consolidation, merger, sale,
transfer, liquidation, dissolution or winding up" with the phrase
"reclassification, consolidation, merger, share exchange, sale, transfer,
division, liquidation, dissolution or winding up."

     10.  Section 27 of the Rights Agreement is amended to read in its entirety
as follows:

     The Company and the Rights Agent shall, if the Company so directs,
supplement or amend any provision of this Agreement without the approval of any
holders of certificates representing shares of Common Stock or Series A
Preference Stock.  From and after the time any Person becomes an Acquiring
Person, the Company and the Rights Agent shall, if the Company so directs,
supplement or amend this Agreement without the approval of any holders of Rights
Certificates in order (a) to cure any ambiguity, (b) to correct or supplement
any provision contained herein which may be defective or inconsistent with any
other provisions herein, or (c) to change or supplement the provisions hereof in
any manner which the Company may deem necessary or desirable and which shall not
adversely affect the interests of the holders of Rights (other than an Acquiring
Person or an Affiliate or Associate of an Acquiring Person).   Without limiting
the foregoing, the Company and the Rights Agent shall, if the Company so
directs, at any time prior to such time as any Person becomes an Acquiring
Person, amend this Agreement to lower the thresholds set forth in the definition
of "Acquiring Person" in Section 1 hereof to not less than 10% (the "Reduced
Threshold"); provided, however, that no Person who (together with all Affiliates
             --------  -------
and Associates of such Person) beneficially owns a number of shares of Voting
Stock equal to or greater than the Reduced Threshold shall become an Acquiring
Person unless such Person shall, after the public announcement of the Reduced
Threshold, increase its (together with all Affiliates and Associates of such
Person) beneficial ownership of the then outstanding shares of Voting Stock
(other than as a result of acquisition of shares of Voting Stock by the Company)
to an amount equal to or greater than the greater of (x) the Reduced Threshold
or (y) the sum of (i) the lowest beneficial ownership of such Person

                                      -3-
<PAGE>

(together with all Affiliates and Associates of such Person) as a percentage of
the outstanding shares of Voting Stock as of any date on or after the date of
the public announcement of such Reduced Threshold plus (ii) .001%.
Notwithstanding the foregoing, (x) after the Stock Acquisition Date or (y) on or
within ninety (90) days of the date of a change (resulting from a proxy or a
consent solicitation or a series of solicitations) in a majority of the
directors of the Company in office at the commencement of such solicitation (or
series of such solicitations), if any Person who is a participant in such
solicitation has stated (or if upon the commencement of such solicitation, a
majority of the directors of the Company has determined in good faith) that such
Person (or any of its Affiliates or Associates) intends to take, or may consider
taking, any action which would result in such Person becoming an Acquiring
Person or which would cause the occurrence of a Triggering Event, any supplement
or amendment shall be effective only if there are Continuing Directors then in
office, and such supplement or amendment shall have been approved by a majority
of such Continuing Directors. Upon the delivery of a certificate from an
appropriate officer of the Company that states that the proposed supplement or
amendment is in compliance with the terms of this Section, the Rights Agent
shall execute such supplement or amendment. Prior to the Distribution Date, the
interests of the holders of Rights shall be deemed coincident with the interests
of the holders of Common Stock and Series A Preferred Stock.

     11.  Section 7 of Exhibit A of the Rights Agreement is amended to replace
the phrase "consolidation, merger, combination or other transaction" with the
phrase "consolidation, merger, combination, division, share exchange or other
transaction."


     12.  This Fourth Amendment to Rights Agreement shall be deemed to be a
contract made under the laws of the Commonwealth of Pennsylvania and for all
purposes shall be governed by and construed in accordance with the laws of such
Commonwealth applicable to contracts to be made and performed entirely within
such Commonwealth, without giving effect to its principles of conflicts of laws.

     13.  This Fourth Amendment to Rights Agreement may be executed in any
number of counterparts, each of which shall be an original, but such
counterparts shall together constitute one and the same instrument.

     14.  Terms not defined herein shall, unless the context otherwise requires,
have the meanings assigned to such terms in the Rights Agreement.

     15.  In all respects not inconsistent with the terms and provisions of this
Fourth Amendment to Rights Agreement, the Rights Agreement is hereby ratified,
adopted, approved and confirmed.  In executing and delivering this Fourth
Amendment to Rights Agreement, the Rights Agent shall be entitled to all the
privileges and immunities afforded to the Rights Agent under the terms and
conditions of the Rights Agreement.


                            [Signature Page Follows]

                                      -4-
<PAGE>

          IN WITNESS WHEREOF, this Fourth Amendment to Rights Agreement has been
duly executed by the Company and the Rights Agent as of the day and year first
written above.



                                    SUNOCO, INC.

(SEAL)
                                    By: /s/ THOMAS W. HOFFMAN
                                        ---------------------
                                        Thomas W. Hoffmann
                                        Vice President and
                                        Chief Financial Officer
Attest:


By: /s/ ANN C. MULE'
    --------------
    Ann C. Mule
    Assistant General Counsel and
    Corporate Secretary
    Sunoco, Inc.


Countersigned:


                                    EQUISERVE TRUST COMPANY, NA
                                    (f/k/a FIRST CHICAGO TRUST
                                    COMPANY OF NEW YORK),
                                    as Rights Agent


                                    By: /s/ ANTHONY MILO
                                        ----------------
                                        Anthony Milo
                                        Manager, Corporate Actions

                                      -5-