Peverley scored his second goal of the game only 1:16 into overtime, and Pavelec stopped 42 shots to help the Thrashers beat Dallas 6-5 on Thursday night for their first home win over the Stars.
Peverley, who added an assist, said credit for the win belonged to Pavelec.
"Our goalie was outstanding tonight," Peverley said, adding Pavelec's play in the net "may be the best performance all year."
Stephane Robidas, who had two goals and an assist for Dallas, didn't know much about the 22-year-old Pavelec before the only game of the season between the teams.
"Whatever his name is, he got some incredible saves tonight," said Robidas after Pavelec earned his first win since Nov. 27 at Carolina.
Pavelec and veteran Johan Hedberg have shared the goaltender position as the Thrashers await the return of Kari Lehtonen, who has had two back surgeries.
Pavelec at times seemed to have too little help on defense as the Stars outshot the Thrashers 47-25.
"I didn't like our game overall, but I loved our competitiveness," Thrashers coach John Anderson said.
Pavelec's collection of glove saves, deflections and other stops seemed to be too little when Loui Eriksson scored for the Stars with only 1:12 remaining in regulation. The goal, which tied the game at 5-5, came only 9 seconds after Dallas coach Marc Crawford pulled goalie Marty Turco for an extra attacker.
Pavelec said Eriksson's shot deflected off the shield on Eriksson's helmet into the net.
"It hit him in the face and went straight into the net," Pavelec said. "It definitely was off his facemask. Those things happen."
Peverley's winner came on a tip-in. He also scored a short-handed goal in the third period.
"We showed a lot of character tonight," Pavelec said. "We needed six goals for the win, but it is huge for us."
The Thrashers improved to 2-10 in the series, including 1-5 in Atlanta. The Thrashers' only other win over the Stars came on Jan. 18, 2006, at Dallas.
Maxim Afinogenov scored on a put-back on Atlanta's power play for a 4-4 tie. Ilya Kovalchuk, Jim Slater and Nik Antropov also scored for the Thrashers.
"They have shooters, and when you have a team like that, you have to match it," Robidas said. "That's not the way we want to play."
The Stars fell to 4-11 in overtime games. Seven of the losses have come in shootouts.
Special teams accounted for most of the scoring. The Thrashers scored three goals on their power play. The Stars had two power-play goals by Robidas and added only their second short-handed goal of the season.
Robidas added an assist but couldn't celebrate his three points. "In a losing game it's unimportant," he said.
The game was tied 4-4 in the third period when a hooking call against Atlanta's Christoph Schubert left Anderson fuming on the bench and set up a Dallas power play.
After Pavelec made a stop against Robidas, Armstrong set up Peverley's short-handed goal for a 5-4 lead with 7:14 remaining in regulation.
Turco stopped seven shots after replacing Alex Auld in the second period.
Jamie Benn and Jere Lehtinen also scored for Dallas.
NOTES: The Stars outshot the Thrashers 17-6 in the first period, 16-9 in the second and 14-9 in the third. ... The Thrashers are 5-3 in overtime games. ... C Brian Sutherby was a healthy scratch for Dallas. ... Slater's goal was his first of the season.