Left wing Ponikarovsky, who assisted in New Jersey's second goal of the game, struck with a backhanded shot on his own rebound with 2:39 remaining to put the Devils in control of the best-of-seven series.
Devils goal-tender Martin Brodeur produced a gritty performance with 25 saves to shade Philadelphia's Ilya Bryzgalov, who made 27 at the other end.
Philadelphia's Brayden Schenn opened the scoring with a wrist shot but the Devils responded with goals just 20 seconds apart from Patrik Elias and Ilya Kovalchuk, who missed Game Two with a lower-body injury, to lead 2-1 after the first period.
Matt Carle tied it for the Flyers in the second period before Zach Parise's wrist shot for the Devils in the third was matched by Philadelphia's Danny Briere, who chipped a rebound over Brodeur's pads, to take the game into overtime.
The Devils, who had scored four third-period goals to blow away the Flyers 4-1 on Tuesday to level the series, killed off two penalties in overtime and outshot the Flyers 31-28 in Game Three.
In the Western Conference, the giant-killing Los Angeles Kings pushed the St Louis Blues to the brink of elimination with a 4-2 home victory in Game Three of their semi-final.
Buoyant after successive road wins, the eighth-seeded Kings scored through Justin Williams, Dwight King, Mike Richards and Drew Doughty to take a commanding 3-0 lead in the best-of-seven series.
"I'm impressed with our team right now," Kings head coach Darryl Sutter said. "It's not about individuals. We didn't give up many shots but we could have managed the puck better in our zone.
"I think we were really good. This was as good of a third period we've played in three months."
Williams opened the scoring with a wrist shot in the first period and, though Chris Stewart replied for the Blues with a backhanded goal early in the second, King and Richards put the home team 3-1 ahead.
Stewart scored his second of the night early in the third period before Doughty sealed the win for the rampant Kings with a slap shot.
Los Angeles goaltender Jonathan Quick made 18 saves and his team are now poised to reach the Western Conference final for the first time since 1993, when they made their only trip to the Stanley Cup Final.
The Kings, who upset the top-seeded Vancouver Canucks in the first round, will aim to sweep the second-seeded Blues in Game Four in Los Angeles on Saturday.