The Reds won for the 80th time this season and remained in solid position to earn at least a wild card berth in the playoffs. They began the night three games behind division-leading Pittsburgh in the National League Central.
Los Angeles has lost back-to-back games and Saturday will try to avoid its first three-game losing streak in almost three months.
Aroldis Chapman struck out the side in the ninth to collect his 35th save.
Cincinnati drew within one when a run scored in the fourth on a double-play grounder off the bat of Ryan Ludwick.
The Reds took the lead in the fifth after almost letting a scoring chance get away. Leake led off the inning with a walk and moved to second on a single by Shin-Soo Choo. Brandon Phillips, however, grounded into a double play with Leake going to third.
That gave reliever J.P. Howell (2-1) a chance to get out of the inning, but Votto hit a 1-0 pitch out to center for the winning blow.