POWER OF ATTORNEY

        Know all by these presents, that the undersigned hereby constitutes and
appoints Trisha Millican, signing singly, with full power of substitution, as
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
        or any rule or regulation of the SEC;

        (2)     execute for and on behalf of the undersigned, in the
        undersigned's capacity as an officer and/or director of Zogenix, Inc.
        (the "Company") and/or 10% holder of the Company's capital stock, Forms
        3, 4, and 5 and any amendments thereto in accordance with Section 16(a)
        of the Securities Exchange Act of 1934 and the rules thereunder;

        (3)     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, complete and execute any amendment or
        amendments thereto, and timely file such form with the SEC and any stock
        exchange or similar authority; and

        (4)     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 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.

        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 18th day of November, 2010.

Signature:  /s/ Ann D. Rhoads
            ---------------------------
Print Name: Ann D. Rhoads