Exhibit 5.1

August 9, 2017

001166.1537

CenterPoint Energy, Inc.

1111 Louisiana

Houston, Texas 77002

Ladies and Gentlemen:

In connection with the issuance by CenterPoint Energy, Inc., a Texas corporation (the “Company”), of $500,000,000 aggregate principal amount of its 2.50% Senior Notes due 2022 (the “Notes”), pursuant to (a) the Registration Statement on Form S-3 (Registration No. 333-215833) (the “Registration Statement”), which was filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), and (b) the related prospectus of the Company dated January 31, 2017, as supplemented by the prospectus supplement of the Company relating to the sale of the Notes dated August 7, 2017 (as so supplemented, the “Prospectus”), as filed by the Company with the Commission pursuant to Rule 424(b) under the Act, certain legal matters with respect to the Notes are being passed upon for you by us. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed with the Commission on the date hereof (the “Form 8-K”).

The Notes are to be issued pursuant to the Indenture, dated as of May 19, 2003, between the Company and The Bank of New York Mellon Trust Company, National Association (successor to JPMorgan Chase Bank, National Association (formerly JPMorgan Chase Bank)), as trustee (the “Trustee”), as supplemented by Supplemental Indenture No. 9 thereto, to be dated as of August 10, 2017 (the “Supplemental Indenture,” and, together with the Base Indenture, the “Indenture”), between the Company and the Trustee.

In our capacity as your counsel in the connection referred to above, we have examined originals, or copies certified or otherwise identified, of (i) the Restated Articles of Incorporation of the Company and the Third Amended and Restated Bylaws of the Company (each as amended to date, the “Organizational Documents”); (ii) the Underwriting Agreement, dated August 7, 2017 (the “Underwriting Agreement”), by and among the Company and the Underwriters named in Schedule I thereto (the “Underwriters”), relating to the issuance and sale of the Notes; (iii) the Registration Statement and the Prospectus; (iv) the Base Indenture and the form of Supplemental Indenture as filed as exhibits to the Form 8-K; and (v) corporate records of the Company, including certain resolutions of the board of directors of the Company, as furnished to us by you, certificates of public officials and of representatives of the Company, statutes and other instruments and documents as we have deemed necessary or advisable for purposes of the opinions hereinafter expressed. In giving the opinions set forth below, we have relied, to the extent we deemed appropriate without independent investigation or verification, upon certificates, statements or other representations of officers or other authorized representatives of the Company and of governmental and public officials with respect to the accuracy of the factual matters

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contained in or covered by such certificates, statements or representations. In giving the opinions below, we have assumed that all signatures on all documents examined by us are genuine, all documents submitted to us as originals are authentic and complete, all documents submitted to us as certified or photostatic copies are true, correct and complete copies of the originals thereof and all information submitted to us was accurate and complete.

On the basis of the foregoing, and subject to the limitations and qualifications set forth herein, we are of the opinion that the Notes will, when duly executed, issued and delivered by the Company in accordance with the terms of the Indenture, authenticated and delivered by the Trustee in accordance with the terms of the Indenture and duly purchased and paid for by the Underwriters in accordance with the terms of the Underwriting Agreement, constitute legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, except as that enforcement is subject to any applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer or conveyance or other laws relating to or affecting creditors’ rights generally, general principles of equity (regardless of whether that enforceability is considered in a proceeding in equity or at law) and any implied covenants of good faith and fair dealing.

The opinions set forth above are limited in all respects to matters of the laws of the State of Texas, applicable federal law of the United States and the contract law of the State of New York. We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Form 8-K. We also consent to the references to our Firm under the heading “Legal Matters” in the Prospectus. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.