"I just went to the net," Gomez said. "I thought he was going to get it in his glove, and it took a bad bounce. I got lucky."
Taking advantage of Hedberg's mishandling of the puck, Gomez put in a backhander for his third winning goal this season and his fifth tally overall.
Rangers coach Tom Renney watched his team fail on its only power-play attempt, dropping New York to 3-for-31 with a man advantage over the last nine games. But the Rangers did improve their puck movement at even strength and on Ryan Callahan's short-handed goal.
"It was a first step back," Renney said. "It's an important two points. The biggest thing for us is to make sure we get up to the net."
The Thrashers have lost five straight at home and have just two victories in 11 games.
Despite eight victories in their last 13, the Rangers have only one win in regulation. They led 2-1 on Callahan's short-handed goal with 18:40 remaining in regulation.
Ilya Kovalchuk, who was trailing Callahan on his goal, redeemed himself 1:29 later by scoring his 10th of the season and second in two games. Skating through the right side of the slot, Kovalchuk redirected Boris Valabik's shot from the left boards for a 2-all tie.
"We had great play from everyone," Thrashers winger Chris Thorburn said. "Everyone went hard, but the outcome did not go our way."
Allowing the first goal for the eighth time in nine games, the Thrashers trailed 1-0 when Hedberg dropped his stick 6:05 into the second and gave up Colton Orr's first goal of the season and first in 83 games.
"We have to look at the bright side," Hedberg said after he made 30 saves but dropped to 5-5-1. "It's a game of breaks. The breaks usually go to the team that works the hardest, and I think we should have won that game."
Atlanta rookie Joey Crabb forced a 1-all tie 6:05 into the second when he scored on a breakaway for his first career goal.
Rangers backup goalie Steve Valiquette, who stretched left to make a difficult glove save on Jason Williams' wrister with 1:31 remaining, stopped 27 shots to improve to 3-2. In the final minute of the first, Valiquette reached up to catch Colby Armstrong's wrister from the left circle.
"We had our chances to win, and it's kind of the way the year has gone so far," Atlanta coach John Anderson said. "If it's a bad bounce, it's going to go against us. I thought we played very hard, and we did what we wanted to do. That's the No. 1 team in their division. We played them right to the end."
Joining Boston as the only other Eastern Conference team with 40 points, the Rangers will need to show the same intensity Friday at New Jersey that they displayed at Philips Arena. New York was admittedly lackluster in getting outscored 15-4 in losing three of its previous four.
"We came out with a lot of energy, and for some reason we got away from good things," Rangers forward Markus Naslund said. "The shifts where we got chances were where we worked hard down low, and they gave the puck up to our defense."
After Valiquette stopped Thorburn's wrister 10:52 into the second, Gomez and Kovalchuk exchanged punches, and both were penalized for roughing. After sitting in the penalty box for four minutes, Gomez and Kovalchuk went after each other again at 17:15 and were sent off for slashing. ... New York improved to 7-2 against the Southeast Division. The Thrashers fell to 2-7 against the Atlantic. ... Orr's previous goal was scored Nov. 21, 2007, at Tampa Bay.