Dion Phaneuf, Mikhail Grabovski and Clarke MacArthur also scored for Toronto, which played another high-scoring game against Atlanta. The teams have combined for 30 goals in three meetings this season.
Dustin Byfuglien, Evander Kane, Nik Antropov and Andrew Ladd scored for the Thrashers.
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 brutal giveaway by Byfuglien, intercepting a pass and beating Ondrej Pavelec between the legs.
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.
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.
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 in 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.
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.
Notes: Toronto scratched D Brett Lebda for the ninth straight game and 26th time this season ... Leafs F Darryl Boyce played with a full face shield. He suffered a serious cut to his nose last week ... Freddy Meyer (upper body), Tobias Enstrom (finger) and Jim Slater (concussion) sat out for the Thrashers ... Atlanta's Freddy Modin left the game with an upper-body injury ... Byfuglien leads the Thrashers with 42 points.