Lee (11-6) threw 84-of-121 pitches for strikes in snapping a nine-start winless streak, yielding five hits and a walk. The left-hander struck out seven en route to the victory.
Jonathan Papelbon finished up with a 1-2-3 ninth for his 22nd save as the Phillies claimed the opener of a four-game series.
Cody Asche's two-run triple in the fourth provided Philadelphia's offense.
New York's Zack Wheeler (6-3) absorbed the loss despite allowing just two runs on five hits over 6 2/3 innings. Like Lee, he walked one and fanned seven.
Andrew Brown got the only RBI for the Mets, who dropped a fifth straight.