It was the fourth career hat trick for Semin, who came in with only two goals in Washington's first seven games after scoring 40 last season. Semin got his first goal in the second period and added two more in the final 15 minutes of regulation.
"He's played hard," Capitals coach Bruce Boudreau said of Semin. "Tonight he got rewarded for playing a good game."
Semin's final goal gave Washington a 3-2 lead with 6:32 remaining, but Atlanta tied it on a shot by Evander Kane with 32.9 seconds left in regulation. Kane's tally came shortly after the Thrashers pulled goalie Chris Mason for an extra skater.
In overtime, however, Fleischmann banged in a rebound of a shot by Eric Fehr to provide the Capitals with their eighth consecutive home win over the Thrashers.
"It was a flukey goal, but it went in," Fleischmann said. "Rebound just ended up on my stick."
Ovechkin came in with a team-high four goals and eight points, and in his career against Atlanta he had 60 points in 37 games. He didn't contribute in this one, and neither did a power play that went 0 for 3 and is scoreless in three straight games.
It didn't matter, because Semin gave Washington all the production it needed in regulation.
"Whenever a player scores, a team needs it. It's not just that they needed my goals tonight," Semin said through an interpreter. "It's been kind of weird for us. We've had a lot of chances, a lot of shots, but we couldn't score and our power play has struggled. Hopefully this will give us a push in the right direction."
Kane scored two goals, Andrew Ladd had one, and Mason finished with 40 saves. But it wasn't enough to prevent the Thrashers from absorbing their third straight defeat.
"You're sad when you lose in overtime, but what a battle," Atlanta coach Craig Ramsay said.
Playing in Washington, where they haven't won since February 2008, the Thrashers were OK with gaining a point.
"You have to get those wins," Kane said, "but at the same time, that point could be huge down the road and into the playoffs. Every point you get means a lot."
Mathieu Perreault had assists on Washington's final two goals in regulation. On the last one, Perreault skated from the right boards between the circles before passing to a wide-open Semin, who put the Capitals up 3-2.
Perreault was making his season debut after being called up from Hershey of the AHL before the game.
"You can't ask for any better," he said. "I know they want me to bring energy to the team."
Michal Neuvirth had 29 saves to help the Capitals snap a two-game skid.
Washington trailed 1-0 before Semin cashed in on a mistake by Mason in the opening minute of the second period. Mason went behind the net and swept the puck around the boards, but Semin intercepted the clearing attempt in the right circle and scored on a drive that glanced off the left pipe.
The Thrashers regained the lead at 4:33 on Kane's first goal of the game.
Semin tied it with 14:51 left, pouncing on the loose puck after Perreault was tripped while skating to the net.
Atlanta outshot the Capitals 13-4 in the first period and took a 1-0 lead when Ladd put in the rebound of his own shot with 58 seconds left and the Thrashers on a power play.
After scoring an NHL-leading 92 goals in first periods last season, the Capitals have been outscored 9-3 in the first frame thus far.
Green returned after a three-game absence due to an undisclosed upper body injury. ... Atlanta's Zach Bogosian (shoulder) was scratched for a fifth straight game. ... Ladd extended his point streak to five games.