Patrik Elias, Ilya Kovalchuk and Zach Parise also scored for the Devils, who killed two penalties in overtime before Ponikarovsky came through with his first goal of the post-season on a backhander that sneaked past Ilya Bryzgalov.
Martin Brodeur made 25 saves for New Jersey. Game 4 is Sunday in New Jersey.
Kovalchuk, who missed Game 2 with a lower body injury, also had two assists in his return, including one on the game winner.
Danny Briere, Matt Carle and Brayden Schenn scored for the Flyers. Bryzgalov had 27 saves.
KINGS 4, Blues 2
LOS ANGELES (AP) — Drew Doughty had a goal and two assists, Jonathan Quick made 18 saves and Los Angeles moved to the brink of an unlikely second-round sweep.
Mike Richards scored the Kings' first power play goal in six games before setting up Doughty's clinching goal with 11:48 to play for the eighth-seeded Kings, who improved to 7-1 in the post-season with their third straight dominant win over second-seeded St. Louis.
Los Angeles could clinch its first trip to the conference finals since 1993 in Game 4 on Sunday.
Chris Stewart scored two goals and Brian Elliott stopped 18 shots in a shaky performance for the Blues, who must accomplish just the fourth comeback from an 0-3 deficit in NHL playoff history to advance.