Kozlov gave the Thrashers the lead, and they finished off the victory when Buffalo leading scorer Thomas Vanek shot wide.
"It was pretty exciting. Nice to get the two points," Lehtonen said. "Those [shootouts] are not so much fun for goalies."
The one thing he appreciated was the break between overtime and the shootout.
"It's good we have two minutes to regroup," Lehtonen said.
The Thrashers snapped a three-game losing streak, and the Sabres fell to 4-0-1.
Buffalo's Jason Pominville scored with 3:08 remaining in the third period to tie it at 2, knocking in his own rebound.
"Somebody on their team turned the puck over and I got in the slot and made a pretty good shot," Pominville said. "I didn't like our start, but as the game went on, it got better."
Pominville's second of the season came after his initial shot bounced high off Lehtonen's glove and back to him.
"I was disappointed for giving up the tying goal just before overtime," Lehtonen said.
The Thrashers got off to a quick 2-0 lead in the first period on goals by Kovalchuk and Bryan Little.
Kovalchuk, a 52-goal scorer last season, netted his second of the season after only 1:35 elapsed. He scored with a hard shot over Lalime's left shoulder.
Little, who leads the Thrashers with four goals, made it 2-0 at 17:12 with another shot over Lalime's left shoulder from about 10 feet out. Todd White assisted on both goals.
"We expected Atlanta to come out hard," Lalime said. "I like how we came back in the second and third. It would have been nice to get the extra point."
Vanek got the Sabres within 2-1 during a two-man advantage with three minutes left in the second period.
Vanek is off to the quickest start of his career, scoring seven goals in Buffalo's first five games. Kotalik and Pominville earned assists.
The Thrashers scratched D Nathan Oystrick and LW Brett Sterling. Buffalo's scratches were C Tim Connolly, D Nathan Paetsch and C Jochen Hecht. ... The Thrashers outshot the Sabres 19-6 in the opening period. ... Buffalo came into the game 18-for-18 on penalty killing and made it 24-for-24 with six stops against Atlanta. The Thrashers, meanwhile, have gone 21 straight power plays without a goal.