Verlander (6-4) allowed three runs on seven hits, issuing a pair of walks before exiting with a 4-3 lead in the seventh.
Jose Valverde turned back a late Pirates rally in the ninth with his sixth save as Detroit reeled off a sixth victory in seven games.
Peralta finished 4-for-4 in the victory. His RBI double in the fifth put the Tigers ahead 4-1 and his run-scoring infield hit in the seventh gave Detroit a 5-3 advantage.
Victor Martinez added two hits, including a two-run double, as the Tigers took the opener of a four-game interleague series.
Pirates starter Francisco Liriano (3-1) absorbed his first loss after three straight triumphs to begin the season. The left-hander allowed four runs on eight hits over five full frames.