Gionta, the Devils' second shooter, beat Johan Hedberg with a backhander. Martin Brodeur, who had 23 saves in regulation, preserved the win with a glove save on Ilya Kovalchuk.
Sergei Brylin and John Madden had New Jersey's goals in regulation.
Todd White and Kovalchuk scored in regulation and Hedberg made 34 saves as the Thrashers lost for the fourth time in the last five games.
The teams exchanged goals in the first period. White struck first with a power-play goal, a tip in of Tobias Enstrom's shot at 14:51.
Brylin tied it for New Jersey with 50.3 seconds remaining. Devils defenseman Paul Martin attacked the Thrashers' net, unloading a close-in backhander that Hedberg blocked. Brylin pounced on the rebound for his first goal in 13 games.
Karel Rachunek, another defenseman, made the key play on the Devils' go-ahead goal at 15:46 of the second. Rachunek faked a shot just inside the blueline and crossed up the defense by continuing down the right wing boards. From deep in the zone, Rachunek fed a pass across the crease to Madden for an easy tap-in goal.
New Jersey dominated the second period with a 12-3 shot advantage.
Atlanta picked up the tempo early in the third as Kovalchuk and Marian Hossa had solid scoring chances.
The pressure paid off Kovalchuk tied the game at 2 at 9:34 with a blast from above the faceoff circles for his league-leading 22nd goal.
Atlanta almost pulled it out in the closing seconds of regulation as White and Hossa swarmed the Devils' net.
Each team had four shots in the overtime but Atlanta had the better chances with Brodeur making a stick stop on Kovalchuk and a glove save against Hossa.
Notes: Devils LW Jay Pandolfo missed a second-straight game with a groin injury.... Brylin is the Devils new ironman with 272 consecutive games played. Pandolfo had played in 307 before the injury.