Devin Mesoraco homered as the Reds won for the ninth time in 11 games. They scored three times in the first inning after Wright let a bases-loaded, two-out grounder skip through his legs.
Leake (4-2) struck out four, walked two and became the latest pitcher to shut down the Mets at Citi Field. New York has lost 10 of 12 at home, rarely scoring many runs.
Leake escaped his biggest jam by retiring slumping Ike Davis on a grounder with runners on second and third to end the fourth.