Harvey (8-2) dominated the Phillies on three hits, didn't issue a walk and struck out 10 in the gem, tossing 75-of-113 pitches for strikes.
The right-hander snapped a personal three-start winless streak and lowered his ERA to 2.23, third-best in the National League.
David Wright and Marlon Byrd bashed back-to-back solo homers in the first inning and Juan Lagares added a three-run shot in the fourth that was originally ruled a double but changed upon video review.
The triumph enabled the Mets to claim their three-game set at Citi Field.
The Phillies' Cliff Lee (10-4) was tagged with the loss, surrendering five runs on seven hits over six frames.