With the Reds trailing 3-2 in the fifth inning, Wilson Valdez and Chris Heisey led off with singles and one out; later Votto lined a pitch just into the right-field stands, putting the Reds ahead to stay.
Cincinnati evened its three-game series at Yankee Stadium, but had to weather a late, two-run New York rally to claim the victory.
Jose Arredondo earned his first save, inducing Curtis Granderson to ground out to end the game with two runners in scoring position.
Heisey and Brandon Phillips each added two hits and an RBI for the Reds.
Homer Bailey (2-3) notched his first victory since April 20, limiting New York to three runs on seven hits over 6 1/3 innings, racking up seven strikeouts while walking only one.
Yankees starter Ivan Nova (4-2) struck out 12 over six innings but was tagged for five runs on seven hits.
Jayson Nix went 3-for-4 with a homer and two RBI in New York's loss.