Blake Wheeler scored on Boston's first shot in the tiebreaker and Thomas stopped all three Montreal attempts to give the Bruins a 3-2 win over the Canadiens, who retired Patrick Roy's No. 33 jersey in a pre-game ceremony, on Saturday night.
Wheeler beat Carey Price on Boston's first attempt when he lost control of the puck as he deked while driving in and momentum kept the puck traveling between the Montreal goalie's legs.
"I might have to practice that now and see if it's a good thing to do, but I'll try to stick with what's worked in the past," Wheeler said.
Thomas, who stopped 33 shots during the game, turned aside Alexei Kovalev, Andrei Markov and Saku Koivu in succession in the shootout to give the Bruins their first regular-season win at the Bell Centre in nearly two years.
"To come in here and come out with a win is really good, especially in a shootout," said Thomas, who didn't see any of Roy's pre-game ceremony. "I've seen Saku score on that last shot and him the one walking off the ice with his arms raised and all happy, and I was happy to be the one with my arms raised and happy today."
Boston improved to 9-0-1 this month and moved into first place overall in the Eastern Conference with 32 points, two ahead of the New York Rangers.
Tom Kostopoulos drew Montreal even at 2 with 3:05 remaining in the third period to the delight of the crowd.
Kostopoulos turned around and used his backhand to deflect defenseman Patrice Brisebois' pass from the right point up and over Thomas' glove into the top-right corner of the net for his second goal of the season.
Canadiens left wing Andrei Kostitsyn opened the scoring with his third goal 1:31 into the second.
"I bet you Milan never thought he was that good that he'd have a shadow on him," Bruins coach Claude Julien said. "I don't know if it's ever happened in his career but it's pretty simple, we've got a good hockey player, he's 20 years old, a first-line player, it's as simple as that."
Matt Hunwick scored midway through the third period to give Boston a 2-1 lead.
The Canadiens lost for the fourth time in six games. Montreal is 3-4-2 since getting off to an 8-1-1 start.
Price made 25 saves.
"He was excellent again tonight," Canadiens coach Guy Carbonneau said. "It's too bad he loses in a shootout when a guy loses the puck. I asked our goalies to give us a chance to win, and both of them have been doing that the last little while."
Lucic drew plenty of attention in the first period.
"Do you think we're going to send him against probably the toughest guy in the league?" said Julien, who told Lucic before the game not to fight. "I know Georges Laraque was doing that because he was told to. Georges is not that type of guy. He respects the young kids, he knows what it's all about. There was no way it was going to happen."
On Friday, Carbonneau said that defenseman Mike Komisarek will be sidelined at least a month because of an upper-body injury -- believed to be to the right elbow -- he suffered during a fight with Lucic on Nov. 13.
"There's more games to come, we'll see how [Lucic] keeps playing," Carbonneau said. "But he was a lot quieter tonight than he was in Boston."
Kostitsyn put Montreal up 1-0 when he scored for the second time in four games 1:31 into the second.
Lucic waved his arms to the crowd after he tied it at 11:11 when he tapped home a pass from Phil Kessel on a 2-on-1 break.
"[Lucic] just went back-door and I was fortunate enough to get it back to him and he buried it," Kessel said.
Petteri Nokelainen appeared to have given Boston the lead with 1:53 remaining in the second but the referee immediately waved it off. Martell ruled that Kessel had made a hand pass when he gloved a puck in the crease, that appeared to strike Price's pad after the Boston forward dropped it to the ice.
Koivu, the Canadiens' captain, delivered a highlight-reel check on Bruins defenseman Dennis Wideman early in the third.
Kovalev lost control of the puck on a two-man break with Tomas Plekanec moments later.
Hunwick scored his second goal of the season 9:41 into the third when he one-timed David Krejci's centering pass and beat Price from the slot.
The Canadiens wore Roy's No. 33 jersey, complete with the Hall of Fame goalie's surname, throughout the pre-game ceremony and during the warmup. ... Bruins D Matt Lashoff was a healthy scratch. ... Boston last won in Montreal on Dec. 4, 2006. ... Canadiens forwards Mathieu Dandenault and Guillaume Latendresse did not dress.