The Reds played from behind most of the night after starter Bronson Arroyo gave up solo home runs to Brandon Belt and Denard Span, but they tied it on Votto's RBI single in the sixth before Cozart's game-winner in the eighth off reliever Hunter Strickland.
Wandy Peralta (2-0) pitched 1 1/3 innings for the win and Raisel Iglesias worked the ninth for his seventh save.
MOMENTS THAT MATTERED
Tightening the Belt: San Francisco's power-starved lineup got a big boost from the return of Span, but it was the solo blast from Belt in the first inning that was most significant.