Carter scored late in the first period to erase a 1-0 Rangers lead and helped out on Claude Giroux's go-ahead, power-play marker midway through the second for the Eastern Conference-leading Flyers.
Wojtek Wolski and Derek Stepan scored for the Rangers, who lost second-leading scorer Marian Gaborik after the first period with an undisclosed injury.
Henrik Lundqvist made 20 saves for New York, which holds the seventh playoff spot in the East.
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