Dustin Byfuglien, Evander Kane, Nik Antropov and Andrew Ladd scored for the Thrashers, who failed to move ahead of Carolina in the Eastern Conference playoff race.
Toronto coach Ron Wilson tinkered with his lines for the first time in roughly a month and seemed to find some chemistry. Frustrated winger Phil Kessel saw his goal drought reach 11 games, but looked good on a new top unit with Grabovski and Kulemin for the final two periods.
They were on the ice when Toronto took its first lead at 4:17 of the third period. Kulemin took advantage of a giveaway by Byfuglien, intercepting a pass and beating Ondrej Pavelec between the legs.
"I had some chances, I was finally plus in a game," said Kessel. "We got the win, right?"
Brent's eventual winner came during a strong shift with Joey Crabb and Colby Armstrong. He scored his seventh of the season from his knees to make it 5-3 at 9:28.
"We look at the standings every day," said Brent. "We don't have room to be complacent."
Ladd converted on a scramble at 11:01 to pull Atlanta to 5-4, but the Thrashers would get no closer.
The Thrashers have been struggling since getting hammered 9-3 by Toronto on Jan. 7, putting together a 2-7-4 record since to fall out of the top eight in the Eastern Conference.
"It's getting to the point where you have to win," said Atlanta coach Craig Ramsay. "We made a very large point of that tonight -- that it wasn't about playing well, it was about winning.
"The vast majority of our players gave everything they had in order to win, but it was those small errors that keep cropping up."
A parade to the penalty box got Atlanta off to a good start against Toronto, which took six minor penalties in the opening 20 minutes and spotted the Thrashers a 2-0 lead.
Kane scored his 14th of the season at 2:39 with a man advantage after the puck bounced off teammate Bryan Little's skate and on to his stick.
Byfuglien made it 2-0 during a 5-on-3 advantage, hammering a point shot past Jean-Sebastien Giguere at 16:14 for his first point since Jan. 2 -- a span of 14 games.
The Leafs came out stronger in the second period and Phaneuf ended a streak of his own with a goal at 1:21. That was his first at Air Canada Centre since joining the Leafs over a year ago.
"It definitely felt good to get that one in here," Phaneuf said.
Grabovski's 22nd of the season with 1 second left on a power play at 4:06 made it 2-2 before Antropov, the former Leaf, put Atlanta back ahead less than a minute later.
MacArthur tied it 3-3 before the intermission by redirecting a nice Tomas Kaberle feed at 15:37. That was his 17th of the season -- matching a career high.
"I think sometimes it's good to shuffle up just to help other guys out or get some excitement back playing with different guys," MacArthur said. "It worked tonight. Whoever you're out there with you've just got to work."
Material from wire services and team media was used in this report.
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