Byfuglien scored his third overtime goal of the season on a power-play at 3:43 of the extra session to give Atlanta a 4-3 victory over the Montreal Canadiens on Sunday.
Byfuglien leads NHL defensemen with 16 goals and 41 points. He has six winning goals.
Tobias Enstrom got his third assist on Byfuglien's winner, a shot into the top right corner that came back out so fast that Thrashers right wing Niclas Bergfors put the puck back in the net for good measure.
"I just bury the head, aim for the back of the net and hope it goes in," said Byfuglien, who leads all NHL defensemen with 16 goals.
Pavelec made 47 saves for Atlanta, which was outshot 50-28.
"He's great every night," Byfuglien said. "He's been stopping pucks for us all year long and that's what we need. He gets the first one and we get the second one for him. Our team's all about having fun, working hard and playing together. We've been doing all right this year."
Pavelec turned aside 15 shots in the first, 16 in the second, and 15 more in the third before stopping the only shot he faced in overtime, the only period in which the Thrashers weren't outshot.
"Some of them were great but some of them, they just tried to put it on the net," said Pavelec, who improved to 14-8-4. "I'm really happy we found a way to win."
Montreal captain Brian Gionta scored with 4:47 left in the third to tie it at 3. The Canadiens got power-play goals from Tomas Plekanec and P.K. Subban, who was called for hooking in overtime.
Carey Price made 24 saves for Montreal, which has lost nine of 12.
"Well, you don't always control the result," Canadiens coach Jacques Martin said. "I think there were a lot of good chances today. We only scored three but sometimes you're going to hit a hot goalie."
Peverley scored his ninth goal 6:20 in to put the Thrashers up 1-0. Enstrom took an open-ice hit from Subban inside the Montreal blue line to make a return pass to Peverley, who drove the left side of the slot to get around Canadiens defenseman Hal Gill and slip a shot between Price's pads.
Plekanec drew Montreal even at 1 with his 12th goal 17:56 in.
Kane gave Atlanta a 2-1 lead with an odd goal 5:42 into the second.
The 19-year-old left wing was sprawled on the ice when he swatted a rebound of Patrice Cormier's shot toward Price, who was hugging the post. Neither team realized that the shot had squeezed through the Montreal goalie until referee Marc Joanette pointed at the net, where the puck was clearly sitting over the goal line.
"I was on my back so I just kind of tried to whack it toward the net," Kane said. "I didn't hear a whistle so I didn't know what was going on. I got up and everybody was celebrating so I was happy it went in."
Subban tied it at 2 when he drove a one-timer from the left point past Pavelec for his third goal at 10:26.
Enstrom got his second assist when Ladd scored his 13th goal with 15.3 seconds left in the second.
Thrashers C Nik Antropov returned after missing five games because of an upper-body injury. ... Canadiens C David Desharnais, recalled from Hamilton of the AHL on Friday, made his season debut.
Copyright by STATS LLC and The Associated Press
Arena: Bell Centre Location: Montreal, Quebec
Referees: Marc Joannette, Kelly Sutherland Linesmen: Jean Morin, Brian Murphy