Mason, who lost his first two starts after being obtained from Columbus this month, turned aside 16-of-17 Rangers tries in the third period as Philadelphia kept its slim post-season chances alive with a second straight win.
Kimmo Timonen supplied a goal and an assist while Jakub Voracek, Brayden Schenn and Erik Gustafsson also scored as the Flyers moved to within five points of New York for the eighth and final Eastern Conference seed.
Philadelphia has five games remaining.
Mats Zuccarello and Derek Stepan tallied for the Rangers, whose two-game winning streak was snapped.
Henrik Lundqvist made 18 saves in the loss.