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.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards