Lecavalier scored two goals in the first period, sandwiched around a tally by Jakub Voracek for a 3-1 Flyers lead.
He added another goal in the third and Matt Read contributed an empty-netter as Philadelphia won a second straight following a four-game losing streak.
Steve Mason turned aside 26-of-28 shots.
Kevin Poulin made 27 saves for New York.
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