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EXHIBIT 5.1

May 12, 2016

Enterprise Products Partners L.P.

1100 Louisiana, 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 a registration statement on Form S-3 (the “Registration Statement”) filed on the date hereof by the Partnership with the Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement relates to the offering of up to 104,963,257 common units representing limited partner interests (the “Common Units”), which may be issued pursuant to the Partnership’s Distribution Reinvestment Plan (the “Plan”). The prospectus contained in the Registration Statement and dated the date of the Registration Statement constitutes the “Prospectus” as used herein. All capitalized terms used but not defined herein have the respective meanings assigned to such terms in the Registration Statement.

As the basis for the opinions 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 to date; (ii) the Sixth Amended and Restated Agreement of Limited Partnership of the Partnership, dated November 22, 2010, as amended to date (the “Partnership Agreement”); (iii) the Certificate of Formation of Enterprise Products Holdings LLC, a Delaware limited liability company and the general partner of the Partnership (the “General Partner”), as amended to date; (iv) the Fifth Amended and Restated Limited Liability Company Agreement of the General Partner, dated effective as of September 7, 2011, as amended to date (the “LLC Agreement”); (v) the Plan; (vi) the Registration Statement; (vii) the Prospectus; and (viii) such other instruments and other certificates of public officials, officers and representatives of the Partnership and the General Partner, 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 and the General Partner 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, the Partnership Agreement, 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 Common Units will be issued and sold in the manner described in the Prospectus 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 Common Units by the Partnership has been duly authorized by the General Partner.

2. Upon the issuance and delivery of the Common 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 as provided in the Plan, (a) such Common Units will be validly issued and (b) purchasers of such Common Units will have no obligation, solely by reason of their ownership of such Units, to make any contributions to the Partnership or any further payments for their purchase of such Common Units, and such purchasers will have no personal liability, solely by reason of their ownership of such Common Units, to creditors of the Partnership for any of its debts, liabilities or other obligations.

We express no opinion other than as to the Delaware Revised Uniform Limited Partnership Act and the Delaware Limited Liability Company Act, 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 and to the reference to this firm under the heading “Legal Matters” in the Prospectus. In giving this consent we do not admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act, or the rules and regulations of the Commission. 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 law.

Very truly yours,

/s/ ANDREWS KURTH LLP