Harvey yielded just two hits and a walk while striking out six before a rain delay ended his stint.
The right-hander tossed 51-of-72 pitches for strikes while notching his ninth start of at least six innings with one or fewer runs this season.
David Wright led the Mets at the plate, going 4-for-5 with a solo homer and two RBI as New York took the rubber match of a three-game series.
Marlon Byrd added two hits and two RBI in the victory.
Phillies starter John Lannan (0-2) was roughed up for six runs (four earned) on eight hits over five full frames.