John Tavares and Casey Cizikas scored 28 seconds apart late in regulation to secure the Islanders' seventh win in nine games.
Michael Grabner also tallied as New York moved into the seventh seed in the Eastern Conference.
Evgeni Nabokov earned the triumph with 26 saves.
Jakub Voracek accounted for Philadelphia's only goal.
Steve Mason, making his first start for the Flyers, stopped 28 shots.