Zajac also had a power-play goal in the second period, and Ilya Kovalchuk added his 25th goal—also on a power play—for New Jersey. The Devils have won five of six and are 21-3-2 since Jan. 8.
Blake Wheeler and Dustin Byfuglien scored for the Thrashers. Atlanta, which has just three regulation wins in its last 33 games, has lost three of five.
Atlanta held leads of 1-0 on Wheeler’s 15th goal in the second and 2-1 on Byfuglien’s 20th goal in the third, but Kovalchuk tied it with 12:09 remaining.
New Jersey is 11th in the Eastern Conference, a point behind the Thrashers.
Wheeler beat Brodeur to the glove side 10:14 into the second with a wrister from the right circle. Andrew Ladd assisted with a pass across the slot.
The next four goals were scored on power plays.
Zajac’s 11th goal, which made it 1-1, came 2:13 later and 1:35 after New Jersey began a two-man advantage courtesy of high-sticking penalties on Atlanta defencemen Tobias Enstrom and Chris Thorburn.
Thrashers goalie Ondrej Pavelec stopped three shots in New Jersey’s 5-on-3 before Patrik Elias passed from the bottom of the right circle and Zajac scored from the left side of the crease.
“It just came down to special teams,” Atlanta coach Craig Ramsay said, “and we didn’t get the job done.”
Byfuglien’s slap shot from the right side of the blue line beat Brodeur’s glove side. The New Jersey bench wanted goalie interference called on Nik Antropov, but it appeared Devils defenceman Colin White knocked down the Atlanta centre while Byfuglien fired the shot.
“He was laying on me when (Byfuglien) shot the puck,” Brodeur said. “He hit my glove, yanked my leg and the net. He’s a guy that does that, but it’s easier to digest when you win the game.”
Kovalchuk, after lifting the puck under the crossbar, celebrated his 10th goal in his last 15 games by slamming into the rear boards with a big smile as Atlanta fans booed their one-time franchise star and No. 1 overall draft pick of 2001.
“It doesn’t bother me,” Kovalchuk said. “Everything I do, they boo me.”
The former Thrashers captain, who was traded to the Devils last season and last summer signed the NHL’s richest contract, had an uncontested look at the net after controlling the rebound of Mark Fayne’s slap shot.
“It was a big goal for us,” Kovalchuk said. “It tied the game. It was nice. It was an easy one.”
On the winning goal, Zajac scored with a wrister beneath the left circle. Kovalchuk began the play and earned an assist with a pass to Elias, who controlled the puck with his skate in the right circle before flicking it across the slot to Zajac.