Miami produced 11 hits, drew two walks and had another batter hit by a pitch. The Marlins, however, were shut out for the seventh time this season and for the third time in their last eight games.
Shin-Soo Choo hit two solo homers and went 4-for-5 with three runs scored. It was Cincinnati's fifth straight win, its longest such streak of the season.
Leake (3-2) struck out six and three relievers closed out the shutout.
Alex Sanabia (2-6) gave up all four runs on nine hits with three walks in six innings. He has dropped five consecutive decisions.