Exhibit 5.1

600 Travis, Suite 4200 Houston, Texas 77002 713.220.4200 Phone 713.220.4285 Fax andrewskurth.com

November 8, 2013

Enterprise Products Partners L.P.

1100 Louisiana Street, 10^th Floor

Houston, Texas 77002

Ladies and Gentlemen:

We have acted as counsel to Enterprise Products Partners L.P., a Delaware limited partnership (the “Partnership”), in connection with the public offering of up to 9,200,000 common units representing limited partner interests in the Partnership (including common units to be issued upon exercise, if any, of the underwriters’ option to purchase additional common units) (the “Common Units”) pursuant to the Partnership’s registration statement on Form S-3 (No. 333-189050), which automatically became effective upon filing with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on July 3, 2013 (the “Registration Statement”). A prospectus supplement dated November 5, 2013, which together with the prospectus filed with the Registration Statement shall constitute the “Prospectus,” has been filed pursuant to Rule 424(b) promulgated under the Securities Act.

As the basis for the opinions hereinafter expressed, we have examined such statutes, including the Delaware Revised Uniform Limited Partnership Act, as amended (the “Delaware Act”), regulations, corporate records and documents, including the Certificate of Limited Partnership of the Partnership, as amended to date, the Sixth Amended and Restated Agreement of Limited Partnership of the Partnership dated as of November 22, 2010, as amended to date (the “Partnership Agreement”), certificates of corporate and public officials, and other instruments and documents as we have deemed necessary or advisable for the purposes of this opinion. In making our examination, we have assumed the genuineness of all signatures on documents examined by us, the authenticity of all documents submitted to us as originals and the conformity with the original documents of all documents submitted to us as certified, conformed or photostatic copies. We have also assumed that all Common Units will be issued and sold in the manner described in the Prospectus and in accordance with the terms of the Underwriting Agreement dated November 5, 2013 relating to the offer and sale of the Common Units (the “Underwriting Agreement”).

Based upon the foregoing, and subject to the limitations and assumptions set forth herein, and having due regard for such legal considerations as we deem relevant, we are of the opinion that (i) the issuance of the Common Units by the Partnership in accordance with the terms of the

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Enterprise Products Partners L.P.

November 8, 2013

Page 2

Underwriting Agreement has been duly authorized by the general partner of the Partnership and (ii) when the Common Units have been issued and delivered in accordance with the terms of the Underwriting Agreement, the Common Units will be validly issued, fully paid (to the extent required under the Partnership Agreement) and non-assessable, except as such non-assessability may be affected by (i) the matters described in the Partnership’s Annual Report on Form 10-K for the year ended December 31, 2012 under the captions “Risk Factors—Risks Relating to Our Partnership Structure” “—Our common unitholders may not have limited liability if a court finds that limited partner actions constitute control of our business” and “—Unitholders may have liability to repay distributions” and (ii) Sections 17-303, 17-607 and 17-804 of the Delaware Revised Uniform Limited Partnership Act.

We express no opinion other than as to the federal laws of the United States of America and the Delaware Act (which is deemed to include the applicable provisions of the Delaware Constitution and reported judicial opinions interpreting those laws).

We consent to the filing by you of this opinion as an exhibit to a Current Report on Form 8-K, and we further consent to the use of our name under the caption “Legal Matters” in the Prospectus. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations issued thereunder. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes of the facts stated or assumed herein or any subsequent changes in applicable law.

Very truly yours,

/s/ ANDREWS KURTH LLP