Marian Hossa made it 1-0 early in the first with his 42nd goal for Atlanta, which increased its lead over idle second-place Tampa Bay to five points in the Southeast Division.
Kozlov gave the Thrashers a 2-1 lead 2:15 into the third period with a tip-in of Andy Sutton's slap shot from the left circle.
Hal Gill made it 2-2 with 13:20 remaining for Toronto, which had won three of four to begin the night two points out of the eighth and final playoff spot in the East.
Losers of the five straight on the road, the Maple Leafs still earned their 85th point, one better than the New York Islanders and Carolina Hurricanes.
John Pohl tied it at 1-1 in the first with his 12th goal.
Kozlov, who scored two goals for a career-high 75 points in a 3-2 overtime loss at Florida on Wednesday night, was in the bottom of the left circle when he swept the puck past the right side of goaltender Andrew Raycroft for his 27th goal.
Nik Antropov's hooking penalty led to Atlanta's man advantage in OT and helped the Thrashers improve to 7-1 in their last eight home games.