Leake (1-0) threw seven scoreless innings and went 3-for-4 at the plate that included an RBI triple. He also scored three runs.
The one-sided victory came after the Reds closed out a 1-0 victory earlier in the day in a game that had been suspended after eight scoreless innings on Tuesday.
Cincinnati finished off a three-game sweep of the Phillies. The Reds came into the series on a five-game losing streak.
Zack Cozart produced three of Cincinnati's 15 hits, one of them being a two-run homer in the fifth inning.
The Reds scored nine times in the first three innings, producing five runs in the second. Todd Frazier hit a solo shot in that frame and Leake delivered his triple that scored Devin Mesoraco.
John Lannan (0-1) retired just five batters while giving up six runs on eight hits.