As a consequence, the Rangers are headed to their first Stanley Cup final in 20 years. And the Canadiens are going home, experiencing a dark cocktail of emotions after falling two wins short.
"We played, in my book, probably our best game of the playoffs," said Rangers coach Alain Vigneault.
The Canadiens didn't. New York outshot Montreal 32-18, with the Habs putting just five shots on goal in the third period of a game that was not as close as the score sounds.
It was a night and day compared to the Canadiens' 7-4 win Tuesday at the Bell Centre.
"It's tough because we're so close. And we're right there," said Montreal defenceman Josh Gorges. "I'm a little bit lost for words because I'm still trying to process this. I'm still stunned. It's tough."
Montreal sniper Max Pacioretty was brutally frank in the wake of the loss.
"A night like tonight, our backs were against the wall," he said. "We've been in that position before but there in the third period it almost seemed like — myself especially — guys were panicking. We got away from our game."
New York really had a go at Montreal in the third, buzzing young goalie Dustin Tokarski's net. The Canadiens did not get a shot on net for the first nine minutes and were back on their heels the entire period.
"The third period, I think we played our best period of the playoffs," said Lundqvist. "When it mattered the most, guys really stepped up."
While the Canadiens missed passes and made bad decisions, the workmanlike Rangers did the little things right. Their finishing could have been better but didn't need to be given Montreal's sputtering offence.
"We gave them one chance in the first, four in the second, and nothing in the third," said Vigneault. "Shouldn't have been a 1-0 game, but you have to give their goaltender a lot of credit. He played outstanding."
So was Lundqvist, who was pulled in the second period of Game 5 after giving up four goals on 19 shots. He returned to world-class form when he needed to be.
The breakthrough came after the Rangers' fourth line bottled the Habs up in their own end near the end of the second period. Boyle, left all alone behind the goal, sent a pass through defenceman Francis Bouillon and Moore snapped a shot past Tokarski on the stick side at 18:07 for his third of the playoffs.
Defenceman Ryan McDonagh also drew an assist, his 10th of the playoffs.
The Rangers' last appearance in the final was 1994 when they defeated the Vancouver Canucks in seven games for their first title in 54 years. The Canadiens have not appeared in the final since 1993 when the dispatched the Los Angeles Kings in five games.
New York will face either defending champion Chicago or the Kings, both formidable foes, as the final kicks off Wednesday in the West.
Vigneault showed faith in his fourth line, starting the game with Moore, Brian Boyle and Derek Dorsett. They repaid him with the key goal on a night that saw the Rangers play with more urgency than the Canadiens before an amped crowd at Madison Square Garden.
Tokarski was busier than Lundqvist but the Swede was spectacular in the second period when he made an amazing circus-like save with his arm and then blocker off Thomas Vanek. The save had a degree of difficulty that would have done an Olympic diver proud as the Rangers goalie, losing his stick in the process, corkscrewed his body to stop the close-range shot that deflected off a diving defenceman.
Asked what he thought of the play, Vigneault replied: "Same thing you did. Wow."
The Rangers scored soon after.
Streamers flew through the air as the final whistle blew. The normally calm Lundqvist threw his arms in the air and was mobbed by his teammates. The crowd chanted "We want the Cup."
With Brad Richards and Martin St. Louis, who won the Cup together a decade ago with Tampa, leading the decision-making process, the Rangers elected not to touch the Prince of Wales Trophy that goes to the Eastern Conference champion.
It's been quite a journey for the Rangers who started the season 3-6 on the road as Madison Square Garden underwent massive renovations. Asked what he would have said if someone had told him in October that his team would go to the Cup final, Vigneault laughed.
"In October?" he asked. "Probably I would have said what are you smoking?"
Vigneault, in his first year as New York's coach, offered a calmer, different message than the fiery John Tortorella. It helped keep the train on track.
Montreal also came together under fire. While there may be cause for celebration down the line, the season ends with regrets and questions.
"We made some big progress this year," said coach Michel Therrien. "I'm proud of this hockey team. We battled hard through the regular season and we battled hard in the playoffs."
Pacioretty pointed to the emotional seven-game win over Boston in the series before.
"You have success against a team like that, maybe you feel too good about yourself," he said. ""It's hard to pinpoint exactly what went wrong. But that could be one of them. Because we feel like we could have matched up pretty good against the Rangers but obviously didn't put up the effort we needed."
Losing the first two games at home proved to be an obstacle Montreal couldn't overcome.
"We played our hearts out for two series and then have a little bit of a letdown this series and it's too late," Pacioretty lamented.
Game 7 would have been Saturday night at the Bell Centre.
For Montreal, it was a disappointing end to a surprising playoff run that won fans across the country as Canada's lone team in the post-season came within two wins of making the Stanley Cup final.
"Let's push for a game 7!" Prime Minister Stephen Harper tweeted before the game.
But the Canadiens, who lost star goalie Carey Price in Game 1, could not rise to the occasion. Therrien said after the game they expected Price would have been ready for Game 1 of the final.
But the Habs had only praise for the 24-year-old goalie they call Ticker.
"Tokarski played unbelievable, especially tonight," said Pacioretty. "That game could easily have been four or 5-0. They outplayed us tonight and he kept us in the game — 1-0 is a very misleading score for that game."
Tokarski said he was proud of his performance, adding he thought everyone on the team felt the same about their play.
"But it's still bitter and it sucks right now," he said.
Tokarski went to the bench with 1:53 remaining and Lundqvist made a big save with his torso.
Montreal used its timeout as Led Zeppelin and then Frank Sinatra rang around the arena.
The win was the 42nd of Lundqvist's playoff career, moving the 32-year-old past Mike Richter for the franchise lead. Richter backstopped the Blueshirts to the '94 Cup.
It was also his ninth playoff shutout, tying him with Richter for the team lead.
Lundqvist has a history of bouncing back from off nights. He was 5-2 with a .930 save percentage in games after a Rangers' loss this post-season.
"It's been tough .. I kept telling myself all day believe in what you're doing," said Lindqvist, looking like he had just walked off the set of "The Great Gatsby" in a charcoal pinstripe suit and plaid tie.
Both teams had to adjust their lineups for Game 6.
Brandon Prust returned from suspension for Montreal but Weise and defenceman Alexei Emelin were both out. Therrien said Weise, flattened by Moore last time out, was not suffering from a head injury but declined to elaborate. Emelin sat out Game 5 with an unannounced injury.
The Rangers came out like men on a mission, outshooting the Habs 4-0 before Montreal captain Brian Gionta was called for goalie interference at 4:15. The Habs were incensed at the call, believing that Gionta was high-sticked on the play.
At one point early on two Canadiens lost their sticks at the same time in their own zone. It took Montreal almost eight minutes to get its first shot on goal, a weak effort from Max Pacioretty.
While Lundqvist lazed, Tokarski was stopping one shot after another — some that he knew very little about. His mask took the brunt of one shot.
The Canadiens didn't get their second shot until some 15 minutes into the period. But it was dangerous, forcing a good Lundqvist blocker save off Alex Galchenyuk as Montreal cooped the Rangers up in their own end.
Montreal was outshot 11-5 in the first period and were lucky not to trail after 20 minutes. Each team had eight shots in the second period.
A slashing penalty to Prust with 5:42 remaining in the game did not help the Montreal cause. But it delighted the crowd.
The rest before the Cup final will be welcomed by the Rangers. They went seven games in each of the previous two rounds, wasting a 3-2 lead against Philadelphia and rallying from 3-1 down to dispatch the Penguins.