Ryan Braun hit a two-run double in the third on which Heisey took a couple of steps in before retreating as the high liner went over his head. The four-year veteran with 134 career starts in left field apparently lost Carlos Gomez's high fly ball to the warning track in the fourth inning that turned into an RBI ground-rule double that made it 4-0.
Peralta (11-6) allowed three hits, including Billy Hamilton's solo homer. Francisco Rodriguez threw a 1-2-3 ninth for his 29th save.
Cincinnati's Mat Latos (2-2) gave up four earned runs and eight hits in seven innings.