Patrik Elias, Ilya Kovalchuk and Zach Parise also scored for the Devils, who killed off two penalties in overtime before Ponikarovsky came through with his first goal of the post-season on a backhander that sneaked past Ilya Bryzgalov on his left side.
"I didn't have time to celebrate because everyone jumped on me right away, but I had a great time in the pile," said Ponikarovsky, whose goal was set up by a wonderful pass from Kovalchuk that forged a 2-on-1 break into the zone.
Martin Brodeur made 25 saves for New Jersey, which will look to take a 3-1 lead in the best-of-7 series here Sunday.
Kovalchuk, who missed Game 2 with a lower body injury, also had two assists in his return with none more important than his pass that caught the Flyers on a bad change.
"You feel pressure," Kovalchuk said after watching the Devils win Game 2 while he nursed a back injury. "The guys played so well, and you don't want to get back in the lineup because you just want to play."
Kovalchuk more than showed he was ready, though.
Danny Briere, Matt Carle and Brayden Schenn tallied for the Flyers. Bryzgalov had 27 saves.
"We're down 2-1, the pressure is on us," Flyers forward Claude Giroux said. "There is no guy on this team that is going to quit. It's going to be a wake-up call.
"We have a good series now."
Schenn nearly won the game eight minutes into overtime with a deflection in front and then the Devils' penalty kill did an outstanding job after a controversial boarding call against Dainius Zubrus with 11:37 left in the overtime and a delay-of-game penalty against Bryce Salvador. New Jersey had problems with its short-handed lines in Round 1 vs. Florida, but the unit that was ranked No. 1 in the regular season appears to have regained its form.
"I think the power play won us a lot of games this year and tonight wasn't the case," Giroux said. "We have to do a better job."
The power play is actually killing the Flyers, who are 2-for-16 in this series after going 12-for-23 against the Penguins.
The Devils seemed on the verge of a 3-2 win early in the third when Parise rammed a puck into the net from in close after Elias won a loose puck behind the net and found the Devils' captain all alone at the right goal post.
Kovalchuk came within inches of making it a two-goal lead minutes later when he had a shot hit off the crossbar as Bryzgalov looked behind him.
Philadelphia tied the game on somewhat of a gift from Brodeur. The Devils' 39-year-old goaltender could not control a weak shot from the outside of the left faceoff circle by James van Riemsdyk, and Briere chipped the rebound over his pads. He has scored goals in five of the Flyers' nine playoff games.
The first two periods were distinct with the Devils dominating the final 11 minutes of the opening session and the Flyers having the upper hand for most of the second.
Carle tied the game at 2-2 at 4:44 of the second with a blast from the top of the left circle that was set up by Jakub Voracek. The forward took a pass along the right boards, skated around the net and found an unguarded Carle coming in from the point for a shot that whizzed by Brodeur.
The goal came minutes after Bryzgalov stopped Adam Henrique on a breakaway to prevent New Jersey from taking a 3-1 lead.
After falling behind 1-0 early, the Devils outshot Philadelphia 10-3 and grabbed the lead when Elias and Kovalchuk tallied in a 20-second span, the fastest two post-season goals in franchise history.
Kovalchuk, the Devils' leading scorer in the regular season, missed Game 2 with a lower body injury. However, he had his legs in the opening period and it paid off for New Jersey.
With Braydon Coburn off for tripping, Elias tied the score with a shot from the right circle that went off Bryzgalov's glove. Kovalchuk snared the secondary assist on the play, sending a pass from the left point to defenceman Marek Zidlicky, who slid it to Elias.
Kovalchuk's goal came on a quick counterattack in which he came late down the middle, took a pass from Travis Zajac and wristed a shot past the Flyers' goalie. The Russian, who had never been part of a winning team in an NHL series until this year's first round vs. the Panthers, pumped his fists and celebrated his fourth goal.
And there was more to celebrate after Parise's go-ahead goal stood.
Schenn had put the Flyers ahead with a power-play goal 6:08 after the opening faceoff. Briere set up Schenn's third post-season goal with a pass from along the goal line that found Schenn low in the left circle. His shot beat Brodeur to the short side.
The Devils have now won three of four overtime contests this post-season, including Games 6 and 7 vs. Florida, when facing elimination. Meanwhile, dating back to their first-round win over Pittsburgh, Philadelphia has now lost consecutive road games.
NOTES: The Flyers didn't make any lineup changes. The Devils did. With Kovalchuk returning, New Jersey sat defenceman Peter Harrold, who had played in all nine previous playoff games. ... The old Devils' record for two fastest playoff goals was 26 seconds by Petr Sykora and Bobby Holik on May 14, 2000 at Philadelphia in the Eastern Conference Finals. That Devils team won the Stanley Cup. ... Flyers C Sean Couturier sustained a lower-body injury in the first period and did not return. ... The crowd of 17,625 was a sellout. ... Devils rookie defenceman Adam Larsson, 19, who scored in his playoff debut in Game 2, remained in the lineup. ... Brodeur will turn 40 on Sunday, in time for Game 4.