Leake allowed six hits and just one run in seven innings of work, forcing weak contact from the Pirate bats that never did too much damage.
Meanwhile, on offense, Zack Cozart, Todd Frazier, Joey Votto and Jay Bruce all knocked solo shots out of the park.
For the Pirates, Andrew McCutchen scored on a Russell Martin double in the sixth inning when Jay Bruce slightly misplayed the ball in right-center field.
The Pirates' Francisco Liriano started and allowed just two runs in six innings, but Bryan Morris allowed two runs out of the bullpen, which allowed the Reds to stretch their lead in the eighth inning.
Aroldis Chapman closed the door on the game in the ninth inning with a two-strikeout save in the ninth inning.
The second game of the series will start at 7:10 p.m. ET tomorrow night from the Great American Ball Park in Cincinnati.