"Everything went wrong," Kovalchuk said. "I don't know what it is. It's unacceptable. It's embarrassing."
Kovalchuk, the former Atlanta captain, scored a power-play goal in the second period for the Devils, who have dropped 11 of 15 overall and eight straight on the road.
Kovalchuk sees no immediate solutions for the team with the NHL's second-worst record.
"Yeah, I mean, what do you think?" said Kovalchuk, who is in the first season of a 15-year, $100 million contract. "We're still 100 points out of the playoffs."
Combined with Washington's loss to Boston, the Thrashers' victory moved them into first place in the Southeast Division.
"Our goal is to be in first place," Boulton said. "We need to keep moving here and building points."
Brodeur, the NHL's career leader in victories, shutouts and games played, lost for the second straight night and has dropped four of five starts since returning from an elbow injury.
"It's been a tough year offensively, defensively and for me personally," Brodeur said. "We're very fragile when we get behind the eight-ball. We have to deal with it."
Johan Hedberg replaced Brodeur (5-14-1), who stopped 11 of 15 shots. Hedberg made four saves on seven shots.
"It's definitely difficult," Brodeur said. "We're all underachieving."
Boulton's second goal of the season, a wrister from the slot 15:30 into the first, made it 2-0.
Boulton was credited with his third goal and his first career multigoal game to put the Thrashers ahead 5-1 with 15:53 remaining. A video review showed that his shot near the right post crossed the goal line before Boulton ran into Hedberg and dislodged the net.
With 3:06 remaining, Boulton scored on a backhander for a 6-1 lead.
"I honestly thought I would not get that last one," Boulton said. "I thought this was too good to be true."
Thorburn assisted on Boulton's first two goals before scoring his fifth with 1:02 left in the game.
Hainsey's first goal, a wrister from the left circle, made it 1-0 at 10:56 of the first. He assisted on Kane's 11th goal, a wrister 16:08 in for a 3-0 lead.
Ondrej Pavelec (11-6-3) made 26 saves for the win.
New Jersey's offense continued to struggle. After recording a season-low 16 shots in a 3-1 home loss to Nashville on Friday, the Devils managed just four shots in the first period. They combined for 23 shots in the second and third but had only Kovalchuk's third goal in three games -- and eighth overall -- to show for it.
"It definitely was embarrassing, but you can't get too high when you win and you can't get too low when you lose," he said.
Facing the team that drafted him No. 1 overall in 2001 but remade its roster after trading him to New Jersey 10 months ago, Kovalchuk was booed repeatedly in his second trip to Philips Arena as an opposing player.
"To me, it's just a regular game," Kovalchuk said. "They played well."
The Devils have dropped 21 of 32 games decided in regulation.
Atlanta D Johnny Oduya, acquired from New Jersey in the Kovalchuk trade, drew an ovation for blocking Patrik Elias' rebound attempt late in the second. ... New Jersey dropped to 5-12 on the road. ... The Devils are 1-14 when trailing after one period and 1-19 when trailing after two. ... The Thrashers are 4-13-4 against New Jersey at home.