Choo's two-run shot in the second inning put the Reds ahead 4-0 and Votto's 470-foot blast off the top of the foul pole with Choo aboard gave Cincinnati a 6-3 advantage in the sixth.
Choo (2-for-3, three runs scored) also provided an RBI double as the Reds -- who came into the contest with a 4 1/2-game lead over Washington for the second National League wild card berth -- evened their three-game series at Miller Park.
Homer Bailey (11-10) went seven innings to get the win, yielding three runs on five hits. He overcame four walks and struck out three.
Milwaukee's Johnny Hellweg (1-4) was tagged for four runs on eight hits in a five-inning stint.
Khris Davis, Carlos Gomez and Jeff Bianchi each drove in a run for the Brewers.