Leake (4-2) scattered three hits, walked two and struck out four in the 99-pitch effort. The right-hander extended his scoreless innings streak to 17 en route to the victory, lowering his ERA to 3.25.
Sam LeCure and Lyle Ondrusek each tossed a shutout frame to complete the Cincinnati's second consecutive win over the Mets and ninth in 11 games overall.
Devin Mesoraco added a solo homer for Cincinnati.
Mets starter Jonathon Niese (3-5) was tagged for just the three unearned tallies over six full frames. He walked three and fanned seven in the loss.