would zhonyas save a sprite?

Yes. Zhonya's Hourglass is a mandatory replacement effect, so when the Sprite's Temporary trigger would kill it at the start of your Beginning Phase, Zhonya's intercedes, kills itself instead, and heals/exhausts/recalls the Sprite to base (Rule 369, 816.1.b).

Two things to keep in mind:

• The Sprite keeps Temporary — base is still the Board, so it never left play. It will die again at the start of your next Beginning Phase, and Zhonya's is already consumed.
• If that Sprite was your only unit on that battlefield, recalling it to base may cause you to lose control of the battlefield during cleanup — and a Hidden Zhonya's left there would be discarded.

This matches FAQ #2 and #8940.