With the scored tied at 3-3 early in the final frame, Atlanta's Dustin Byfuglien had the puck near his own net and tried to make a pass but put it directly on the stick of Kulemin, who whipped a quick shot past Ondrej Pavelec.
Tim Brent added another Leafs goal midway through the frame that proved to be decisive when Andrew Ladd found the net for Atlanta less than 2 minutes later, making it a one-goal game.
Clarke MacArthur and Mikhail Grabovski donated a goal and an assist each for the Maple Leafs and Dion Phaneuf also scored to back Jean-Sebastien Giguere's 30 saves.
Byfuglien, Evander Kane and Nik Antropov also scored for the Thrashers, who have gone 0-4 since the all-star break.
Pavelec let in five goals on 32 shots.
Celebrity Families of 2014 [PHOTOS]