The Indians had pulled even 2-2 in the top of the frame on a pinch-hit solo homer from Jason Giambi.
But the Reds quickly struck against reliever Nick Hagadone (0-1) in the next half-inning. Shin-Soo Choo singled to lead off and one out later Votto lifted a shot into the first row of the left-field bleachers for the decisive blow.
Aroldis Chapman struck out two in the ninth for his 13th save as the Reds took the opener of a three-game rivalry series with their ninth victory in 12 games overall.
Ubaldo Jimenez surrendered two runs on four hits over seven full innings for the struggling Indians, who fell for the sixth time in seven contests.