The Devils took a 2-1 advantage in the Eastern Conference semifinals, getting the winning goal from a player who began the season in Carolina and is playing with his fourth team in three seasons.
New Jersey also got a goal from Ilya Kovalchuk, who missed the second game of the series with a lower body injury.
The Devils will host the fourth game of the series Sunday.
Kovalchuk got the puck to Ponikarovsky in the New Jersey zone as Philadelphia was in the midst of a line change. Ponikarovsky sped down the right wing on a 2-1 and put a shot on goal.
Bryzgalov stopped the shot, but Ponikarovsky put in the rebound on his backhand.
Ponikarovsky spent his first eight NHL seasons with Toronto, but then played a year for Pittsburgh and another with Los Angeles before winding up with Carolina to start the 2011-12 campaign.
He was dealt from the Hurricanes to New Jersey 49 games into the season.
Brayden Schenn opened the scoring for the Flyers, but Patrik Elias and Kovalchuk tallied 20 seconds apart late in the first period to give New Jersey the lead. Matt Carle produced the only second-period goal for Philadelphia to forge a 2-2 tie.
Brodeur, who posted his 105th career playoff victory, made 25 saves. Bryzgalov stopped 27-of-31 shots.