Fister (5-1) rebounded from poor outing in a Thursday loss to Washington, controlling the Astros on five hits. The right-hander didn't allow a walk and struck out seven.
The Tigers erased a 2-0 deficit with three runs in the fifth, capped by Andy Dirks' RBI ground-rule double.
Houston starter Lucas Harrell (3-4) was reached for five runs on seven hits in five frames.
J.D. Martinez had an RBI for the Astros.