Exhibit 1.1

ONEOK PARTNERS, L.P.

AMENDMENT NO. 1 TO EQUITY DISTRIBUTION AGREEMENT

January 23, 2013

This Amendment No. 1 (this “Amendment”) to the Equity Distribution Agreement, dated as of November 13, 2012 (the “Agreement”), by and between ONEOK Partners, L.P., a Delaware limited partnership (the “Partnership”) and Citigroup Global Markets Inc. (the “Manager”, and together with the Partnership, the “Parties”), is entered into on and as of January 23, 2013. Capitalized terms used and not defined in this Amendment have the meanings ascribed thereto in the Agreement.

WHEREAS, the Partnership filed a registration statement on Form S-3 (File Number 333-185959), which was declared effective on January 23, 2013 (the “New Registration Statement”), pursuant to which it wishes to sell the Units available for issuance and sale under the Agreement;

WHEREAS, the Parties wish to amend certain terms of the Agreement to reference the New Registration Statement and make certain related corresponding changes; and

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, it is agreed as follows:

Section 1. Amendments to Agreement.

(a) Section 2(a) of the Agreement is hereby deleted in its entirety and replaced with the following:

“The Partnership meets the requirements for use of Form S-3 under the Act and has prepared and filed with the Commission a registration statement (File Number 333-185959) on Form S-3, including a related Base Prospectus, for registration under the Act of the offering and sale of the Offered Units of the Partnership. Such Registration Statement, including any amendments thereto filed prior to the Execution Time or prior to any such time this representation is repeated or deemed to be made, has become effective. The Partnership has filed with the Commission the Prospectus Supplement relating to the Offered Units in accordance with Rule 424(b). As filed, the Prospectus contains all information required by the Act and the rules thereunder, and, except to the extent the Manager shall agree in writing to a modification, shall be in all substantive respects in the form furnished to the Manager prior to the Execution Time or prior to any such time this representation is repeated or deemed to be made. The Registration Statement, at the Execution Time, each such time this representation is repeated or deemed to be made, and at all times during which a prospectus is required by the Act to be delivered (whether physically or through compliance with Rule 172 or any similar rule) in connection with any offer or sale of Offered Units, meets the requirements set forth in Rule 415(a)(1)(x). The initial Effective Date of the Registration Statement was not earlier than the date three years before the Execution Time. Any reference herein to the Registration Statement, the Base Prospectus, the Prospectus Supplement, any Interim Prospectus Supplement or the Prospectus shall be deemed to refer to

and include the documents incorporated by reference therein pursuant to Item 12 of Form S-3 which were filed under the Exchange Act on or before the Effective Date of the Registration Statement or the issue date of the Base Prospectus, the Prospectus Supplement, any Interim Prospectus Supplement or the Prospectus, as the case may be; and any reference herein to the terms “amend,” “amendment” or “supplement” with respect to the Registration Statement, the Base Prospectus, the Prospectus Supplement, any Interim Prospectus Supplement or the Prospectus shall be deemed to refer to and include the filing of any document under the Exchange Act after the Effective Date of the Registration Statement or the issue date of the Base Prospectus, the Prospectus Supplement, any Interim Prospectus Supplement or the Prospectus, as the case may be, deemed to be incorporated therein by reference.”

(b) Section 2(d) of the Agreement is hereby deleted in its entirety and replaced with the following:

“intentionally omitted”

(c) Section 4(a) of the Agreement is hereby deleted in its entirety and replaced with the following:

“During any period when the delivery of a prospectus relating to the Offered Units is required (including in circumstances where such requirement may be satisfied pursuant to Rule 172) to be delivered under the Act, the Partnership will not file any amendment of the Registration Statement or supplement (including the Prospectus Supplement or any Interim Prospectus Supplement) to the Base Prospectus or any Rule 462(b) Registration Statement relating to the Offered Units unless the Partnership has furnished to the Manager a copy for its review prior to filing and will not file any such proposed amendment or supplement to which the Manager reasonably objects, unless (i) in the judgment of counsel to the Partnership, such filing is required by applicable law or (ii) is advisable in furtherance of a Commission request. The Partnership has properly completed the Prospectus, in a form approved by the Manager, and filed such Prospectus, as amended at the Execution Time, with the Commission pursuant to the applicable paragraph of Rule 424(b) by the Execution Time and will cause any supplement to the Prospectus to be properly completed, in a form approved by the Manager, and will file such supplement with the Commission pursuant to the applicable paragraph of Rule 424(b) within the time period prescribed thereby and will provide evidence satisfactory to the Manager of such timely filing. The Partnership will promptly advise the Manager (i) when the Prospectus, and any supplement thereto, shall have been filed (if required) with the Commission pursuant to Rule 424(b) or when any Rule 462(b) Registration Statement shall have been filed with the Commission, (ii) when, during any period when the delivery of a prospectus (whether physically or through compliance with Rule 172 or any similar rule) is required under the Act in connection with the offering or sale of the Offered Units, any amendment to the Registration Statement shall have been filed or become effective, (iii) of any request by the Commission or its staff for any amendment of the Registration Statement, or any Rule 462(b) Registration Statement, or for any supplement to the Prospectus or for any additional information, (iv) of the issuance by the Commission of any stop order suspending the effectiveness of the Registration Statement or of any notice objecting to its use or the institution or threatening of any proceeding for that purpose and (v) of the receipt by the Partnership of any notification with respect to the suspension of the qualification of the Offered Units for sale in any jurisdiction or the institution or threatening of any proceeding for such purpose. The Partnership will use its reasonable best efforts to prevent the issuance of any such stop order or the occurrence of any such suspension or objection to the

use of the Registration Statement and, upon such issuance, occurrence or notice of objection, to promptly use its reasonable best efforts to obtain the withdrawal of such stop order or relief from such occurrence or objection, including, if necessary, by filing an amendment to the Registration Statement or a new registration statement and using its reasonable best efforts to have such amendment or new registration statement declared effective as soon as practicable.”

(d) Section 6(i) of the Agreement is hereby deleted in its entirety and replaced with the following:

“intentionally omitted”

(e) Definitions.

(i) The definition of “Base Prospectus” in Section 18 of the Agreement shall be deleted in its entirety and replaced with the following:

“Base Prospectus” shall mean the base prospectus referred to in Section 2(a) above contained in the Registration Statement at January 23, 2013.”

(ii) The definition of “Effective Date” in Section 18 of the Agreement shall be deleted in its entirety and replaced with the following:

“Effective Date” shall mean each date and time that the Registration Statement, any post-effective amendment or amendments thereto and any Rule 462(b) Registration Statement became or becomes effective.

(iii) The definition of “Prospectus Supplement” in Section 18 of the Agreement shall be deleted in its entirety and replaced with the following:

“Prospectus Supplement” shall mean the most recent prospectus supplement relating to the Offered Units that was first filed pursuant to Rule 424(b) at or prior to January 23, 2013.”

(iv) The definition of “Registration Statement” in Section 18 of the Agreement shall be deleted in its entirety and replaced with the following:

“Registration Statement” shall mean the registration statement referred to in Section 2(a) above, including exhibits and financial statements and any prospectus supplement relating to the Offered Units that is filed with the Commission pursuant to Rule 424(b) and deemed part of such registration statement pursuant to Rule 430B, as amended on each Effective Date and, in the event any post-effective amendment thereto or any Rule 462(b) Registration Statement becomes effective, shall also mean such registration statement as so amended or such Rule 462(b) Registration Statement, as the case may be.”

(v) The following definitions of “Rule 462” and “Rule 462(b) Registration Statement” shall be added to Section 18 of the Agreement:

“Rule 462” refers to such rule under the Act.

“Rule 462(b) Registration Statement” shall mean a registration statement and any amendments thereto filed pursuant to Rule 462(b) relating to the offering covered by the registration statement referred to in Section 2(a) hereof.

(vi) The definition of “Well-Known Seasoned Issuer” in Section 18 of the Agreement shall be deleted in its entirety.

Section 2. Effectiveness. This Amendment shall be effective as of the date hereof for all future offers and sales under the Agreement.

Section 3. Representations and Warranties. The Partnership represents to the Manager that it has duly authorized, executed and delivered this Amendment.

Section 4. Continuing Effect. Except as expressly amended by this Amendment, the Agreement remains in full force and effect in accordance with its respective terms and is hereby in all respects ratified and confirmed.

Section 5. References to Agreements. All references to the Agreement in the Agreement or in any other document executed or delivered in connection therewith, shall, from the date hereof, be deemed a reference to the Agreement as amended hereby.

Section 6. Applicable Law. This Amendment shall be governed by and construed in accordance with the law governing the Agreement.

Section 7. Counterparts. This Amendment may be signed in one or more counterparts, each of which, when executed and delivered, shall constitute an original and all of which together shall constitute one and the same agreement.

[SIGNATURE PAGE FOLLOWS]

IN WITNESS WHEREOF, the Parties have caused this Amendment to be duly executed as of the date first above written.

Amendment to Equity Distribution Agreement