Kovalchuk connected on a breakaway at 3:51 of the third to snap a 1-all tie, as Atlanta handed Chicago its third straight loss.
After losing their first six games this season, the Thrashers are 3-2 in their last five.
Chicago’s Patrick Kane, the NHL’s first overall draft pick last summer, scored a power-play goal. Jason Williams scored a power-play goal with 1:09 left to cut it to 3-2 and set up Kane’s goal.
Chicago rookie Jonathan Toews also assisted on Kane’s goal to extend his point streak to nine games. Toews, who missed Chicago’s first two games with a broken finger, has a point in each contest he’s played so far.
Atlanta’s Johan Hedberg made 29 saves. Lalime blocked 19 shots.
Kozlov deflected Kovalchuk’s shot from the top of the left circle and past Lalime during a 5-on-3 Atlanta advantage at 10:06 of the first period to open the scoring.
Kane’s power-play goal at 5:08 of the second tied it at 1. He beat Hedberg on the short side with a shot from the right circle after taking William’s cross-ice pass.
Kovalchuk converted a breakaway at 3:51 of the third to give Atlanta a 2-1 lead. Following a Chicago turnover, he broke in alone down right wing from center ice and beat Lalime with a shot between the legs.
Kozlov made it 3-1 at 7:53. Kovalchuk picked off a pass at the right point off the Chicago zone, then fed it to Kozlov who was alone in front of Lalime.
Williams scored a power-play goal through a screen with Lalime on the bench for an extra attacker with 1:09 left to complete the scoring.Notes: Chicago LW Dave Koci missed his first game on injured reserve with a broken nose. Blackhawks D Andrei Zyuzin sat out with a pulled hip muscle. ... Chicago recalled C Dave Bolland from Rockford of the AHL for Saturday’s game. ... Atlanta G Kari Lehtonen missed his fourth game with a groin strain. ... Chicago’s healthy scratches were LW Sergei Sansonov and D Danny Richmond. Atlanta’s were D Steve McCarthy, LW Pascal Dupuis and LW Brett Sterling.