Bruce also supplied a first-inning RBI single to open the scoring for the Reds, who rapped out 12 hits in the one-sided affair.
Zack Cozart went 2-for-3 with three RBI as third-place Cincinnati clinched the three-game series.
The triumph temporarily pulled the Reds within two games of National League-leading St. Louis while also allowing them to maintain a 4 1/2-game advantage over Washington in the NL wild card race.
Leake (14-6) scattered five hits in the dominating start, lowering his ERA to 3.21. The right-hander walked two and struck out six.
Houston's Jordan Lyles (7-8) was scorched for nine runs (eight earned) on nine hits in a 3 1/3-inning effort.