SECTION 16
                                POWER OF ATTORNEY

KNOW ALL MEN BY THESE PRESENTS, that the undersigned hereby constitutes and
appoints each of Joseph Wm. Foran, David Lancaster, Nathan Pekar and Kyle Ellis,
signing singly, the undersigned's true and lawful attorney-in-fact to:

        (1)  execute for and on behalf of the undersigned, in the
             undersigned's capacity as an officer and/or director of Matador
             Resources Company (the "Company"), Forms 3, 4 and 5 in
             accordance with Section 16(a) of the Securities Exchange Act of
             1934, as amended, and the rules thereunder;

        (2)  do and perform any and all acts for and on behalf of the
             undersigned which may be necessary or desirable to complete and
             execute any such Form 3, 4, or 5 and timely file such form with
             the United States Securities and Exchange Commission and any
             stock exchange or similar authority; and

        (3)  take any other action of any type whatsoever in connection with
             the foregoing which, in the opinion of such attorney-in-fact,
             may be of benefit to, in the best interest of, or legally
             required by, the undersigned, it being understood that the
             documents executed by such attorney-in-fact on behalf of the
             undersigned pursuant to this Power of Attorney shall be in such
             form and shall contain such terms and conditions as such
             attorney-in-fact may approve in such attorney-in-fact's
             discretion.

The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 30th day of January, 2012.

                                          /s/ Matthew V. Hairford
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                                         Matthew V. Hairford