<PAGE>   1
                                                                  Exhibit 10.1.1




                               THIRD AMENDMENT TO
                                CREDIT AGREEMENT


         This THIRD AMENDMENT TO CREDIT AGREEMENT (the "Third Amendment") is
dated as of the 27th day of October, 2000 by and among DAIRY MART CONVENIENCE
STORES, INC., a Delaware corporation (the "Company"), the banks and other
financial institutions listed on Schedule I to the Credit Agreement (as
hereinafter defined)(collectively, together with any banks or financial
institutions from time to time parties to the Credit Agreement, the "Banks") and
CITIZENS BANK OF CONNECTICUT, a Connecticut stock savings bank, as agent for the
Banks (in such capacity, the "Agent").

                              W I T N E S S E T H:

         The Company, the Banks, and the Agent are parties to a certain Credit
Agreement dated as of the 28th day of December, 1999 (as amended and in effect
from time to time, the "Credit Agreement") whereby the Banks agreed to make
loans and advances and otherwise extend credit to the Company.

         The Company, the Banks, and the Agent amended the Credit Agreement in
certain respects pursuant to a certain First Amendment to Credit Agreement dated
as of the 28th day of January, 2000 and a certain Second Amendment to Credit
Agreement dated as of the 28th day of July, 2000 (collectively, the "Prior
Amendments").

         The Company, the Banks, and the Agent desire to further amend the
Credit Agreement.

         Section 10.1. of the Credit Agreement provides that no amendment,
supplement or modification of the Credit Agreement shall be effective unless the
same shall be in writing and signed by the Company, the Banks and the Agent.

         NOW, THEREFORE, in consideration of one dollar ($1.00) and other good
and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the Company, the Banks and the Agent hereby agree as follows:

1. DEFINED TERMS. Defined terms not defined herein shall have the meanings
ascribed to them in the Credit Agreement.

2. AMENDMENT TO CREDIT AGREEMENT.

         (i) The definition of the term "CLEAN-DOWN PERIOD" is hereby amended
and restated in its entirety as follows:

         "CLEAN-DOWN PERIOD" means the period commencing on July 1 and ending on
September 30 of each year during the Commitment Period.

<PAGE>   2
                                       2



         (ii) Section 2.11 of the Credit Agreement, entitled MANDATORY
PREPAYMENTS; CASH COLLATERALIZATIONS, is hereby amended by adding the following
thereto as a new subsection (c):

         (c) Notwithstanding any provision of this Section 2.11 to the contrary,
         the Company shall, not later than March 15, 2001, whether through (x)
         the public issuance or private placement of debt or equity securities
         of the Company or any Subsidiary, (y) an Asset Disposition or (z)
         otherwise, make prepayments on the Loans in the amount or amounts set
         forth on Exhibit A to this Third Amendment.

         (iii) Section 2.16 of the Credit Agreement, entitled ANNUAL CLEAN-DOWN
OF REVOLVING CREDIT LOANS, is hereby amended and restated in its entirety as
follows:

         The Company shall, during each Clean-Down Period, reduce the
         outstanding aggregate principal amount of Revolving Credit Loans to
         zero and maintain such zero balance for at least 30 Consecutive Days
         during each such Clean-Down Period. This Section 2.16 shall not affect
         any Letters of Credit which are issued and outstanding prior to the
         Clean-Down Period nor the Company's right to request the issuance of
         additional Letters of Credit during the Clean-Down Period.

         (iv) Subsection (a) of Section 7.1 of the Credit Agreement, entitled
ADJUSTED CONSOLIDATED INDEBTEDNESS TO CONSOLIDATED EBITDA, is hereby amended and
restated in its entirety as follows:

         (a) ADJUSTED CONSOLIDATED INDEBTEDNESS TO CONSOLIDATED EBITDA. For any
         period of four consecutive fiscal quarters ending on any FQED set forth
         below, permit the ratio of (i) Adjusted Consolidated Indebtedness at
         the end of such period less Store Properties Held For Sale/Leaseback at
         the end of such period to (ii) Consolidated EBITDA for such period to
         be more than the ratio set forth opposite such FQED:

<TABLE>
<CAPTION>

                           FQED                                                     RATIO
                           ----                                                     -----

<S>                                                                             <C>
         The FQED ending on or about October 30, 2000                           4.87 to 1.00
         The FQED ending on or about January 31, 2001 and thereafter            3.90 to 1.00
</TABLE>


<PAGE>   3

                                       3

         (v) Subsection (b) of Section 7.1 of the Credit Agreement, entitled
EBITDA TO INTEREST EXPENSE, is hereby amended and restated in its entirety as
follows:

         (b) EBITDA TO INTEREST EXPENSE. For any period of four consecutive
         fiscal quarters ending on any FQED set forth below, permit the ratio of
         (i) Consolidated EBITDA for the applicable period to (ii) Consolidated
         Interest Expense for such period to be less than the ratio set forth
         opposite such FQED:

<TABLE>
<CAPTION>
                           FQED                                                     RATIO
                           ----                                                     -----

<S>                                                                             <C>
         The FQED ending on or about October 30, 2000                           1.64 to 1.00
         The FQED ending on or about January 31, 2001 and thereafter            2.25 to 1.00
</TABLE>

         (vi) Subsection (c) of Section 7.1 of the Credit Agreement, entitled
FIXED CHARGE COVERAGE, is hereby amended and restated in its entirety as
follows:

         (c) FIXED CHARGE COVERAGE. For any period of four consecutive fiscal
         quarters ending on any FQED set forth below, permit the ratio of (i)
         Consolidated EBITDAR minus the amount of any federal, state and local
         income taxes levied by a Governmental Authority on the revenues of the
         Company which are actually paid by the Company or its consolidated
         Subsidiaries in cash during such period, to (ii) Consolidated Interest
         Expense, plus all principal payments required to be made during the
         period on account of any Consolidated Indebtedness, plus the amount of
         any Consolidated Rent Expense during the period, to be less than the
         ratio set forth opposite such FQED:

<TABLE>
<CAPTION>
                           FQED                                                    RATIO
                           ----                                                    -----

<S>                                                                             <C>
         The FQED ending on or about October 30, 2000                           1.16 to 1.00
         The FQED ending on or about January 31, 2000 and thereafter            1.25 to 1.00
</TABLE>

3. AMENDMENT FEE. In consideration of the agreement of the Banks to execute and
deliver this Third Amendment, the Company shall pay to the Agent for the ratable
benefit of the Banks an amendment fee in the amount and at the time set forth on
Exhibit A to this Third Amendment.

4. CONFIRMATION OF AGREEMENTS. The Company, the Banks, and the Agent hereby
agree that, except as provided in this Third Amendment, the Credit Agreement (as
amended by the Prior Amendments), the Notes and the Loan Documents, and the
grant of the liens, security interests and other encumbrances thereunder, and
their agreements, covenants, obligations, representations and warranties
thereunder and therein are hereby expressly ratified, confirmed and restated as
of the date hereof.

5. EFFECT OF AMENDMENT. The Company, the Banks, and the Agent hereby agree that,
except as provided in this Third Amendment, the Credit Agreement (as amended by
the Prior Amendments) remains in full force and effect and has not been modified
or amended in any respect, it being the intention of the Company, the Banks, and
the Agent that this Third


<PAGE>   4
                                       4


Amendment and the Credit Agreement (as amended by the Prior Amendments) be read,
construed and interpreted as one and the same instrument.

6. BENEFIT. This Third Amendment shall inure to the benefit of and bind the
parties hereto and their respective successors and assigns.

7. AMENDMENTS. This Third Amendment shall be modified only in writing, executed
by all parties hereto.

8. COUNTERPARTS. This Third Amendment may be executed in any number of
counterparts, each of which when so executed and delivered shall be deemed to be
an original and all of which counterparts, taken together, shall constitute but
one and the same instrument.

9. EFFECTIVENESS. This Third Amendment shall become effective as of the date of
the execution and delivery by each of the Company, the Banks, and the Agent of a
counterpart of this Third Amendment, and, in the case of the Company, its
delivery to the Agent or its legal counsel of telephonic (confirmed in writing),
written, facsimile or telex notice (actually received) that the same has been
signed and delivery thereof arranged for (by mail, overnight courier or hand
delivery) (the "Effective Date").

                          [SIGNATURE PAGE FOLLOWS NEXT]



<PAGE>   5

                                       5


         IN WITNESS WHEREOF, the parties hereto have executed this Third
Amendment as of the Effective Date.

                                  DAIRY MART CONVENIENCE STORES, INC.



                                  By:  /s/ GREGORY G. LANDRY
                                       -----------------------------------
                                       Name:  Gregory G. Landry
                                       Title: Executive Vice President and
                                              Chief Financial Officer

                                  CITIZENS BANK OF CONNECTICUT,
                                  Individually and as Agent



                                  By:  /s/ SCOTT S. BARNETT
                                       -----------------------------------
                                       Name:  Scott S. Barnett
                                       Title: Vice President


                                  NATIONAL CITY BANK



                                  By:  /s/ LAWRENCE J. HANNAN
                                       -----------------------------------
                                       Name:  Lawrence J. Hannan
                                       Title: Senior Vice President

                                  PROVIDENT BANK



                                  By:  /s/ JAMES M. HOJNACKI
                                       -----------------------------------
                                       Name:  James M. Hojnacki
                                       Title: Vice President