Exhibit 5.1

2001 ROSS AVENUE DALLAS, TEXAS 75201-2980   TEL +1 214.953.6500 FAX +1 214.953.6503 BakerBotts.com AUSTIN BEIJING BRUSSELS DALLAS DUBAI HONG KONG HOUSTON LONDON MOSCOW NEW YORK PALO ALTO RIYADH SAN FRANCISCO WASHINGTON

June 1, 2020

Zix Corporation

2711 North Haskell Avenue

Suite 2200, LB 36

Dallas, Texas 75204-2960

Ladies and Gentlemen:

We have acted as counsel to Zix Corporation, a Texas corporation (the “Company”), with respect to certain legal matters in connection with the Registration Statement on Form S-3 (the “Registration Statement”) filed on or about the date hereof by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the offer and sale by the selling stockholders identified therein (the “Selling Stockholders”) from time to time pursuant to Rule 415 under the Securities Act of (i) 100,206 shares of the Company’s Series A Convertible Preferred Stock, par value $1.00 per share (the “Series A Preferred Shares”) and (ii) 23,372,873 shares of the Company’s common stock, par value $0.01 per share (the “Common Shares” and together with the Series A Preferred Shares, the “Securities”) issuable during the effectiveness of the Registration Statement upon conversion of the Series A Preferred Shares. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above, we have examined originals, or copies certified or otherwise identified, of the Restated Articles of Incorporation of the Company and the Second Amended and Restated Bylaws of the Company, each as amended to date, the Series A Certificate of Designations establishing the Series A Preferred Stock filed with the Secretary of State of the State of Texas on February 15, 2019 (the “Series A Certificate of Designations”), corporate records of the Company, including minute books of the Company as furnished to us by the Company, certificates of public officials and of representatives of the Company, statutes, including the Texas Business Organizations Code, as amended (the “TBOC”), and other records, certificates, documents and instruments that we have deemed necessary or appropriate for purposes of rendering the opinions set forth below.

In connection with rendering the opinions set forth below, we have assumed that (i) the Registration Statement and any amendments thereto (including post-effective amendments) will have become effective; (ii) all Securities will be offered and sold in compliance with applicable federal and state securities laws and in the manner specified in the Registration Statement and any applicable prospectus supplement to the Prospectus; (iii) the certificates for the Securities will conform to the specimens thereof examined by us and will have been duly countersigned by a transfer agent and duly registered by a registrar of such Securities, or, if uncertificated, valid book-entry notations will have been made in the register of the Company in accordance with the provisions of the governing documents of the Company; and (iv) each document submitted to us for review is accurate and complete, each such document that is an original is authentic, each such document submitted to us as a copy conforms to the original of such document and all signatures on each such document are genuine.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that:

1. the Series A Preferred Shares to be sold by the Selling Stockholders have been duly authorized and are validly issued, fully paid and nonassessable; and

2. With respect to the Common Shares issuable upon conversion of the Series A Preferred Shares (the “Conversion Shares”), such Conversion Shares have been duly authorized by the Company and validly reserved for issuance upon such conversion and, when issued and delivered upon such conversion in accordance with the terms of the Series A Certificate of Designations, will be validly issued, fully paid and nonassessable.

The foregoing opinions are limited in all respects to the TBOC, as published in effect on the date hereof, and applicable reported judicial decisions, rules and regulations interpreting and implementing the TBOC. We express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our Firm under the heading “Legal Matters” in the Prospectus forming a part of the Registration Statement. In giving this consent, we do not hereby 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 of the Commission thereunder.

Very truly yours,

/s/ Baker Botts L.L.P.