Power of Attorney

    Know all by these presents, that the undersigned hereby constitutes and
appoints each of Paul M. Johnston and Frank E. Day, signing singly, the
undersigned's true and lawful attorney-in-fact to:

    (1) prepare, execute in the undersigned's name and on the undersigned's
        behalf, and submit to the U.S. Securities and Exchange Commission (the
        "SEC") a Form ID, including amendments thereto, and any other documents
        necessary or appropriate to obtain codes and passwords enabling the
        undersigned to make electronic filings with the SEC of reports required
        by Section 16(a) of the Securities Exchange Act of 1934, as amended (the
        "Exchange Act"), and the rules and regulations thereunder;

    (2) execute for and on behalf of the undersigned Forms 3, 4 and 5 (including
        amendments thereto) in accordance with Section 16(a) of the Exchange,
        and the rules and regulations thereunder;

    (3) do and perform any and all acts for and on behalf of the undersigned
        that may be necessary or desirable to complete and execute any such Form
        3, 4 or 5, complete and execute any amendment or amendments thereto,
        file that Form with the SEC and any stock exchange or similar authority,
        and provide a copy as required by law or advisable to such persons as
        the attorney-in-fact deems appropriate; and

    (4) take any other action of any type whatsoever in connection with the
        foregoing that, in the opinion of the attorney-in-fact, may be of
        benefit to, in the best interest of, or legally required of the
        undersigned, it being understood that the documents executed by the
        attorney-in-fact on behalf of the undersigned pursuant to this Power of
        Attorney will be in such form and will contain such terms and conditions
        as the attorney-in-fact may approve in the 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 the attorney-in-fact, or the attorney-
in-fact's substitute or substitutes, will 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, and their
substitutes, in serving in such capacity at the request of the undersigned, are
not assuming, nor is Montage Resources Corporation, any of the undersigned's
responsibilities to comply with Section 16 of the Exchange Act.

    The undersigned agrees that each such attorney-in-fact may rely entirely on
information furnished orally or in writing by or at the direction of the
undersigned to the attorney-in-fact. The undersigned also agrees to indemnify
and hold harmless Montage Resources Corporation and each such attorney-in-fact
against any losses, claims, damages or liabilities (or actions in these
respects) that arise out of or are based upon any untrue statements or omissions
of necessary facts in the information provided by or at the direction of the
undersigned, or upon the lack of timeliness in the delivery of information by or
at the direction of the undersigned, to that attorney-in-fact for purposes of
executing, acknowledging, delivering or filing any Form 3, 4 or 5 (including any
amendment thereto) and agrees to reimburse Montage Resources Corporation and the
attorney-in-fact on demand for any legal or other expenses reasonably incurred
in connection with investigating or defending against any such loss, claim,
damage, liability or action.

    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 Montage
Resources Corporation, 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 the date written below.

                                                      /s/ Oleg E. Tolmachev
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                                                                       Signature

                                                       Oleg E. Tolmachev
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                                                                     Print Name

                                                          March 4, 2019
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                                                                            Date