The Thrashers snapped a five-game losing streak to stretch their lead back to five points over the second-place Hurricanes in the Southeast Division.
Kozlov and Hossa scored on Atlanta's first two attempts in the shootout, while Atlanta goalie Kari Lehtonen stopped Carolina's Ray Whitney and Justin Williams. Lehtonen finished with 24 saves.
Bobby Holik forced the overtime with a goal from the blue line at 10:27 of the third period. He beat Carolina goalie Cam Ward, who tried to atone for the long goal with three saves on Ilya Kovalchuk in overtime. Ward had 23 saves.
The Thrashers led 1-0 and 2-1 in the first period, but allowed the Hurricanes, who lost for the first time in four games, to come back.
Williams and Whitney scored the first two goals for Carolina, which lost for the first time in four meetings with Atlanta this season.
Defenceman Dennis Seidenberg, acquired in a trade with Phoenix on Jan. 8, put the Hurricanes ahead 3-2 just 27 seconds into the third period. His shot from the right circle bounced off of goalie Lehtonen and in front of a diving Garnet Exelby.