Phillip Danault and Zachary Bolduc also scored for the Canadiens, who are the No. 3 seed from the Atlantic Division. Jakub Dobes made 37 saves.
“I actually felt really good this game,” said Dobes, who was pulled midway through the third period of an 8-3 loss in Game 6 after allowing six goals on 33 shots. “... I think me getting pulled at home was kind of a wake-up call. I took it personal. And we won today, so I’m really happy.”
Montreal will face the Carolina Hurricanes, who are the No. 1 seed from the Metropolitan Division, in the Eastern Conference Final. Game 1 of that best-of-7 series will be in Raleigh, North Carolina, on Thursday (8 p.m. ET; TNT, HBO Max, truTV, SN, CBC, TVAS).
“Last year's experience in the playoffs (a first-round loss in five games to the Washington Capitals), what we're going through right now, you can't buy that,” Canadiens coach Martin St. Louis said. “It's amazing. I'm so happy for the players to live that.
“It's unreal to play in the NHL, but to get to live this do-or-die situation, in terms of moving on or you're done, scoring the big goal in overtime, that feeling that a player has, it's unbelievable. I'm so happy that we're getting to live that.”
Rasmus Dahlin and Jordan Greenway scored for the Sabres, who were the No. 1 seed from the Atlantic. Luukkonen made 22 saves.
“It hurts. I told the team it hurts,” Buffalo coach Lindy Ruff said. “That pain will go away, but I won’t let this one game define the season we had. I told the players how proud I was of them. The battle that we took into Game 6 in Montreal, and then we came back here and gave ourselves every chance to win. So, this one game doesn’t define our season for us.”
Danault gave Montreal a 1-0 lead at 4:30 of the first period when Kaiden Guhle’s centering pass deflected off his right skate and past the left pad of Luukkonen. The play started after Josh Anderson won a race for the puck with Bowen Byram below Buffalo's goal line.