Montreal's Artturi Lehkonen scored the winning goal 1:39 into overtime and the Canadiens advanced to the Stanley Cup Final for the first time since 1993 by beating Vegas 3-2 Thursday in the NHL playoffs.
The 25-year-old Finnish left wing fired the puck high past Golden Knights goaltender Robin Lehner to give Montreal a four games to two victory in the best-of-seven semi-final series.
"It's a pretty good feeling," Lehkonen said. "Just trying to go high and hit the net.
"We were confident. We just stuck to it. We knew at some point it was going to go in."
The Canadiens, 500-1 longshots when the playoffs began, will play for the Stanley Cup against the winner of Friday's seventh-game semi-final showdown between the New York Islanders and defending champion Tampa Bay Lightning.
"We tried not to look ahead," Lehkonen said. "It's a big win for us. We've got four more to go."
Montreal became the first Canadian team to reach the Stanley Cup Final since the Vancouver Canucks in 2011.
No Canadian team has won the NHL crown since Montreal in 1993, but the Canadiens have won a record 24 NHL titles.
Only 3,500 were allowed in the Bell Centre but thousands more were gathered outside the arena to watch on a huge videoscreen and everyone erupted in cheers when Lehkonen delivered the winner early in the extra period.
Montreal goaltender Carey Price made 37 saves while Lehner made 29 in a losing cause.
Canadiens captain Shea Weber opened the scoring 14:06 into the first period on an unassisted power-play goal, intercepting a clearing attempt and firing the puck past Lehner.
Reilly Smith equalized for Vegas only 48 seconds later, deflecting in a shot off the left post and it was 1-1 after one period.
Montreal rookie Cole Caufield, a 20-year-old American who in March won the Hobey Baker Award as the top player in US college hockey, put the Canadiens back on top with a goal off a wrist shot 9:36 into the second period.
Again the Golden Knights answered, with Alec Martinez scoring 68 seconds into the third period to pull Vegas level at 2-2 and force the extra session.