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EXHIBIT 5.1

November 26, 2014

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 Partnership’s registration statement on Form S-4, as amended (the “Registration Statement”), filed with the Securities and Exchange Commission (the “SEC”) on November 26, 2014, pursuant to the Securities Act of 1933, as amended (the “Securities Act”). This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

The Registration Statement relates to the issuance by the Partnership of up to 36,827,557 common units (the “Common Units”) representing limited partner interests in the Partnership, pursuant to the Agreement and Plan of Merger, dated as of November 10, 2014 (the “Merger Agreement”), by and among the Partnership, Enterprise Products Holdings LLC, a Delaware limited liability company and the general partner of the Partnership (the “General Partner”), EPOT MergerCo LLC, a Delaware limited liability company, Oiltanking Partners, L.P., a Delaware limited partnership (“Oiltanking”), and OTLP GP, LLC, a Delaware limited liability company and the general partner of Oiltanking.

In rendering the opinions set forth herein, we have examined and relied on originals or copies, certified or otherwise identified to our satisfaction, of (i) the certificate of limited partnership and the agreement of limited partnership of the Partnership, (ii) the certificate of formation and the limited liability company agreement of the General Partner, (iii) the Merger Agreement and (iv) such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinions set forth herein. In our examination, we have assumed, without independent investigation (a) the genuineness of the signatures on all documents that we have examined, (b) the legal capacity of all natural persons, (c) the authenticity of all documents supplied to us as originals, (d) the conformity to the authentic originals of all documents supplied to us as certified, photostatic or faxed copies and (e) the authenticity of the originals of such latter documents. We have also assumed that all the Common Units issued pursuant to the Merger Agreement will be issued in the manner described in the proxy statement/prospectus included in the Registration Statement and in accordance with the terms of the Merger Agreement.

Our opinions expressed herein are limited to the Delaware Revised Uniform Limited Partnership Act and the Delaware Limited Liability Company Act, and we express no opinion as to the laws of any other jurisdiction.

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Enterprise Products Partners L.P.

November 26, 2014

Page 2

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that when the Common Units have been issued and delivered in accordance with the terms of the Merger Agreement, (a) such Common Units will be validly issued and (b) recipients of such Common Units will have no obligation, solely by reason of their ownership of such Common Units, to make any contributions to the Partnership or any further payments for their acquisition of such Common Units, and such recipients 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 consent to the filing by you of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in proxy statement/prospectus included in the Registration Statement. In giving this consent, we do not thereby 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 SEC. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in law.

Very truly yours,

/s/ ANDREWS KURTH LLP