Leake (7-3) controlled the Pirates on one run over six hits, allowing one walk and striking out three.
After leaving with a 2-1 lead, Sam Lecure and Tony Cingrani combined for a scoreless top of the eighth to maintain the advantage.
Cincinnati then padded the lead with solo homers from Joey Votto and Jay Bruce in next half-inning and Aroldis Chapman wrapped up the win with his 18th save as the Reds moved 1 1/2 games ahead of Pirates for second place in the National League Central.
Todd Frazier and Zack Cozart also belted bases-empty blasts for Cincinnati, which took the first of a four-game set.
Bucs starter Francisco Liriano (5-3) absorbed the loss, allowing two runs on five hits over six full frames.
Russell Martin provided Pittsburgh's only RBI.