EXHIBIT 5.1

600 Travis, Suite 4200 Houston, Texas 7700 713.220.4200 Phone andrewskurth.com 713.220.4285 Fax

October 1, 2013

Enterprise Products Partners L.P.

1100 Louisiana Street, 10th Floor

Houston, Texas 77002

Ladies and Gentlemen:

We have acted as special counsel to Enterprise Products Partners L.P., a Delaware limited partnership (the “Partnership”), in connection with the preparation of the registration statement on Form S-8 (the “Registration Statement”) to be filed with the Securities and Exchange Commission (the “Commission”) in connection with the registration by the Partnership under the Securities Act of 1933, as amended (the “Securities Act”), of the sale of up to 25,000,000 additional common units (the “Units”) representing limited partner interests in the Partnership which may be issued pursuant to the 2008 Enterprise Products Long-Term Incentive Plan (Third Amendment and Restatement) (the “Plan”).

As the basis for the opinion hereinafter expressed, we have examined and relied on originals or copies, certified or otherwise identified to our satisfaction, of the following: (i) the Certificate of Limited Partnership of the Partnership, as amended; (ii) the Sixth Amended and Restated Agreement of Limited Partnership of the Partnership, as amended (the “Partnership Agreement”); (iii) the Certificate of Formation of Enterprise Products Holdings LLC (formerly named EPE Holdings, LLC), a Delaware limited liability company and the general partner of the Partnership, as amended (the “General Partner”); (iv) the Fifth Amended and Restated Limited Liability Company Agreement of the General Partner, as amended (the “LLC Agreement”); (v) the Plan; (vi) the Registration Statement; and (vii) such other instruments and other certificates of public officials, officers and representatives of the Partnership and such other persons as we have deemed appropriate as a basis for the opinions set forth herein.

In rendering the opinions expressed below, we have assumed and have not verified (i) the genuineness of the signatures on all documents that we have examined, (ii) the legal capacity of all natural persons, (iii) the authenticity of all documents supplied to us as originals and (iv) the conformity to the authentic originals of all documents supplied to us as certified, photostatic or faxed copies. In conducting our examination of documents, we have assumed the power, corporate or other, of all parties thereto other than the Partnership to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the due execution and delivery by such parties of such documents and that, except as set forth in the numbered opining paragraphs below, to the extent such documents purport to constitute agreements, such documents constitute valid and binding obligations of such parties.

We have also assumed that (A) the Certificate of Limited Partnership of the Partnership and the Partnership Agreement and the Certificate of Formation of the General Partner and the LLC Agreement, in each case as amended to date, will not have been amended in any manner that would affect any legal conclusion set forth herein, and (B) all Units will be issued and sold in the manner described in the prospectus related to the Plan and in accordance with the terms of the Plan.

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:

1. The issuance of the Units by the Partnership has been duly authorized by the General Partner.

2. Upon the issuance and delivery of the Units from time to time in accordance with the terms of the Plan for the consideration established by the Plan and the satisfaction of any performance conditions associated therewith and any requisite determinations by or pursuant to the authority of the Board of Directors of the General Partner or a duly constituted and acting committee thereof as provided in the Plan, such 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 Related 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, as amended (the “Delaware LP Act”).

We express no opinion other than as to the Delaware LP Act (which is deemed to include the applicable provisions of the Delaware Constitution and reported judicial opinions interpreting those laws) and the federal laws of the United States of America, and we are expressing no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent we do not admit that we are “experts” under the Securities Act, or the rules and regulations of the Commission thereunder, with respect to any part of the Registration Statement, including this exhibit. 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, and we have assumed that at no future time would any such subsequent change of fact or law affect adversely our ability to render at such time an opinion (a) containing the same legal conclusions set forth herein and (b) subject only to such (or fewer) assumptions, limitations and qualifications as are contained herein.

Very truly yours,

/s/ ANDREWS KURTH LLP