No team has been to the Stanley Cup Final more than the Montreal Canadiens. Now they stand one victory away from a 35th appearance and their first in 28 years.

Carey Price made 26 saves to lead Montreal to a 4-1 victory over the Vegas Golden Knights on Tuesday night, putting the Canadiens one step closer to the Stanley Cup Final.

"You know, it’s the oldest cliché in hockey, but the fourth one’s going to be the hardest and we’re fortunate to have the opportunity at home and we’ll be ready to go in Game 6," said Eric Staal, whose second-period goal held up as the game-winner.

The Canadiens, who last won the Stanley Cup in 1993, lead Vegas 3-2 in their best-of-seven series, with Game 6 scheduled for Bell Centre in Montreal on Thursday.

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Jesperi Kotkaniemi, Cole Caufield and former Golden Knight Nick Suzuki also scored for the Canadiens, whose 11th playoff victory is the franchise’s most in one postseason since the 1993 championship run, also the last time a Canadian-based team won the title.

The Canadiens, who rallied from a 3-1 series deficit in the first round against Toronto and swept Winnipeg in the second round, shook off Sunday’s home loss in Game 4 to win for the second time in Las Vegas.

"I think that’s what our mindset has been this whole playoff, is getting to do what we do, regardless of what happens," Staal said. "I don’t think we change much. We do what we do every single shift, every moment we have, every opportunity we have to try and be difference makers for our team."

Meanwhile, as Max Pacioretty was the only one to score for Vegas, the storyline remained the same with Vegas struggling to find its offense against Montreal’s suffocating tactics, in limiting space and dominating the neutral zone. The Golden Knights had 56 shot attempts, with 12 missing the target and 17 others being blocked.

Marc-Andre Fleury, the league’s active leader in playoff wins (90) and games played (162), made 22 stops in front of an announced crowd of 17,969 that were left stunned with the Golden Knights now on the brink of elimination.

The Golden Knights, who have scored 11 goals in the series, have gotten just four from their forwards.

"You can point to a lot of things - we just weren’t sharp in our execution, in our decisions and it cost us," Golden Knights coach Peter DeBoer said. "We’ve got to find a way. You’ve got to find a way this time of year against the good teams, and against pressure, and against tension, against a good goalie. Those are the teams that end up standing at the end of the day."

Montreal’s forwards continued to stand tall, scoring all four goals in the win.

Kotkaniemi was the beneficiary of strong defensive play in Vegas’ offensive zone, as Montreal defensemen Jeff Petry and Jon Merrill created a turnover to push the puck in transition. Josh Anderson streaked past Vegas defenseman Zach Whitecloud and pulled Fleury to his far right with a backhand that was stuffed. The rebound floated to Fleury’s left, where Kotkaniemi was in position to backhand the puck into a wide-open net to give Montreal a 1-0 lead.

Suzuki, who was dealt to Montreal in the trade that sent Pacioretty to Vegas, set the Canadiens up for a two-goal lead in the second period with a perfectly timed backcheck on Jonathan Marchessault to the right of Price. At the other end, Suzuki’s patience paid off, as he waited until the precise moment to feed Staal between the hashmarks for a wrist shot that beat Fleury top shelf.

With the confidence level clearly headed in opposite directions by the midway point of the second period, and the Canadiens feeding off momentum on a power play, another Vegas turnover ended up in transition with Corey Perry darting in on a would-be breakaway before shuffling the puck cross-ice to Caufield, who one-timed a snap shot up top to extend Montreal’s lead to 3-0.

Pacioretty got Vegas on the board after he whiffed on an initial shot near the top of the circle, then followed up with a wrist shot over Price’s blocker to cut the deficit to two, at 3-1.

It was all the Golden Knights would get, as Price stopped the final nine shots he saw, and Suzuki - who never got to suit up for one regular-season game with the Golden Knights - made an empty-net goal to provide the final margin.

"We responded well and stayed under control," Suzuki said. "They had their chances. We had great back pressure, great sticks and turning a lot of pucks over in the neutral zone."

Teams that win Game 5 when a best-of-7 NHL semifinal is tied have a series record of 47-15 (.758).