Zach Parise and Jamie Langenbrunner also scored for the Devils while Brian Rafalski had three assists.
Mike Knuble scored twice for the Flyers.
Gionta put the Devils ahead at 3:33 of the final period. Positioned at the top of the crease, Gionta deflected Rafalski's shot between the pads of Antero Nittymaki.
It was the second straight game that Gionta came up big in the third period. He scored all the goals as the Devils overcame a three-goal third period deficit Thursday in a 7-6 shootout victory over Toronto.
It was a solid night for Brodeur, who rebounded after surrendering five second-period goals against the Maple Leafs.
The teams exchanged power-play goals in the first period.
New Jersey scored first at 9:08 when Parise rifled a shot from the right circle past Nittymaki.
Philadelphia countered at 11:14 as Knuble cut to the net and took a feed from Peter Forsberg to beat Brodeur. The power-play tally was a rare development for the Flyers who were 3-for-32 with the man advantage through the first four games.
Both teams added a goal in the second period.
Knuble scored again to give the Flyers a 2-1 lead at 1:23 as he knocked in Geoff Sanderson's pass through the crease.
Langenbrunner pulled the Devils even with their second power-play score with 1:41 remaining in the period. Langenbrunner, in the high slot, deflected Rafalski's point shot.
Notes: The morning skate for both teams at Continental Airlines Arena was cancelled due to a water-main break on Route 120, the highway that runs past the arena. The break, which occurred Friday afternoon, was repaired by 1:30 p.m. Saturday. ... Nittymaki made his fourth straight start for the Flyers; Brodeur has started all four games for the Devils. ... Philadelphia kicked off a four-game road trip which continues with games against Buffalo, Tampa Bay and Florida. ... Devils defenceman David Hale remains sidelined with an eye injury suffered in practice on Sept. 29. ... Devils captain Patrik Elias played in his 600th game.