Hossa had his third assist on Kozlov's second goal of the game 1:48 into overtime, lifting Atlanta to a 3-2 win over the Ottawa Senators on Monday.
Kozlov gave the Thrashers a 2-1 lead midway through the second period, then outmaneuvered Ottawa defenseman Joe Corvo in overtime to receive Hossa's pass before beating Ray Emery with a backhander between the legs on a breakaway with a delayed penalty signaled against the Senators.
"It was a race and I was the first one on the puck," Kozlov said. "It was a little bit lucky but it worked for us."
Kari Lehtonen stopped 33 shots to send Atlanta to its sixth win in seven games. The Thrashers lost 4-1 in Buffalo on Saturday to end their second five-game winning streak of the season.
"I think it's nice to have a win on the first day of the new year, especially since we bounced back after the game in Buffalo," Kozlov said. "We played very well against Buffalo, but we made a couple of mistakes and it cost us that game. That was a very solid game for us. Kari made some good saves and I thought we deserved to win."
Senators defenseman Tom Preissing scored Ottawa's second power-play goal on a slap shot from the point 16:05 into the third to tie it at 2.
"Obviously it's a big win for us," Thrashers head coach Bob Hartley said. "It's never easy to come and play in this rink. After the game in Buffalo the other night, I think we wanted to get back on the winning track. It was a hard-fought battle."
Hossa -- the Thrashers' leading scorer with 24 goals, 31 assists and 55 points -- also set up second-period goals by Ilya Kovalchuk and Kozlov to end his former team's four-game winning streak.
Traded by Ottawa to Atlanta before last season, Hossa assisted on Kovalchuk's power-play goal 4:51 into the second period to tie the game at 1. Kozlov's first goal came at 11:16.
"We tried to set up Kovy for a one-timer," Hossa said. "He's got that cannon and there was a good screen in front of the net so that was a big goal for us, especially on the power play. On the second goal I tried to shoot low and in, and he gave up a rebound. And on the third one I saw Kozlov hanging at the red line and fired it off the boards and he did all the work."
Senators captain Daniel Alfredsson scored Ottawa's other power-play goal in the opening minute of the second period.
Emery made 26 saves for the Senators, who lost for the first time in five games since losing high-scoring center Jason Spezza to a knee injury.
"We definitely battled, and played the type of game we wanted to, as well," Emery said. "For the most part I think we outplayed them and out-chanced them, so it's a frustrating one to lose, especially when you come back like that. At least we got a point out of it and there were some positive signs out there."
Atlanta had a potential goal waved off 14:18 into the third when the referees determined that Emery had been pushed into the net by Thrashers forward Jason Krog.
Hartley didn't understand why the goal was denied, and wasn't satisfied with the explanation he was given.
"We watched the replay," Hartley said. "Krog, you can see that he definitely gets cross-checked and the puck is in the net, but the referee told us that Krog was on top of the goalie so he probably didn't see the puck, but I don't know."
Ottawa, which also recently lost center Mike Fisher to a knee injury, was missing its top three centers. Antoine Vermette didn't play because of a hip he injured in Saturday's 3-2 overtime win in Toronto.
"The way we battled back is encouraging," Alfredsson said. "Maybe the referee missed a call on their goal, but that's the way it goes."
Former Senators defenseman Shane Hnidy, whose holding penalty led to Preissing's goal, prevented an Ottawa goal in the first when he stopped a loose puck from crossing the goal line with his stick and swiped it under Lehtonen.
After Alfredsson beat Lehtonen for his 11th goal, Kovalchuk scored his 21st goal when he one-timed a slap shot past Emery from the left point on a crisp passing play begun by Hossa and continued by defenseman Niclas Havelid.
Hossa also played a prominent role in giving Atlanta a 2-1 lead midway through the middle period. Kozlov got his 16th goal when he netted a rebound of Hossa's shot.
- Hossa has gotten 27 of his 55 points on the power play.
- C Serge Payer joined the Senators' lineup after he was recalled from Binghamton of the AHL on an emergency basis earlier in the day.
- Ottawa C Josh Hennessy played his third straight game since also being an emergency call-up Friday.