Now they're one win away from hosting a Game 7 for the right to go to the Stanley Cup Final.
The Canadiens chased New York Rangers goalie Henrik Lundqvist in the second period and won a wild Game 5, 7-4 at Bell Centre. Bourque scored two of Montreal's three second-period goals and their first in the third.
"It's just nice," he said. "I think most importantly, obviously, was to extend the series and get a win for our team, and I was just happy to have a good game."
The Rangers lead the best-of-7 series 3-2 with Game 6 at Madison Square Garden on Thursday (8 p.m. ET; NBCSN, CBC, RDS). Game 7 would be Saturday at Bell Centre.
New York has not won a Stanley Cup Playoff series in fewer than seven games since the 2008 Eastern Conference Quarterfinals (five games against the New Jersey Devils). Montreal has twice come back to win a series after trailing 3-1; the last time was the 2010 Eastern Conference Quarterfinals against the Washington Capitals.
"[The Canadiens] probably got a little bit of hope, I would imagine, but it doesn't change how we think," Rangers center Brad Richards said. "We have to worry about ourselves and our game plan. We don't play like that and we won't play like that next game. Great situation coming home. We've won two of three here [in Montreal]; sometimes they're bound to get some bounces and they created them. It's a tough building to win three in a row in. So we'll go home and be a lot better structurally and detailed-wise in our building."
Bourque, who had one goal in his previous 10 games, bracketed his two goals in the second period around the Rangers' three in a span of 4:24.
"He loves this time of year," Montreal forward Brendan Gallagher said of Bourque. "He comes out and he's a competitor. He's enjoying the opportunity we have. And he's a leader. He's leading by example out there to score not only three goals, but very timely goals. It was big."
"It was just nice to get that lead again," Bourque said. "We worked hard to get the 4-1 lead and they played well, they came back ... and that was an important goal for our team."
Bourque scored his hat trick goal at 6:33 of the third, putting Montreal ahead 6-4. It was the first hat trick by a Canadiens player in a conference final since Guy Lafleur on May 1, 1975 against the Buffalo Sabres. Montreal had not scored seven goals in a playoff game since defeating the Hartford Whalers 7-4 on April 27, 1992.
"He was a force out there," Montreal coach Michel Therrien said of Bourque. "On the forecheck, he took the man. He was moving his feet. He was going hard to the net. He's a very good scorer, so definitely that was a great performance by him."
Rick Nash, Derek Stepan and Kreider scored consecutive goals for the Rangers after coach Alain Vigneault replaced Lundqvist (four goals allowed on 18 shots against) with Talbot 8:58 into the second period.
"I was just not good enough," Lundqvist said. "It's hard to analyze it this quickly, but it was a combination of a couple of things. We start the game with taking a penalty and it kind of puts us on our heels a little bit. Just bottom line all of us need to be better, starting with me."
Vigneault said he didn't consider putting Lundqvist back in the game for the start of the third period with the Rangers trailing 5-4. Afterward, Lundqvist sounded like he didn't want to go in.
"It was better to keep Talbot in there, for me to get a little break there and start thinking about the next one," Lundqvist said. "Of course I was hoping for us to get back in the game, and we got close, but now we're going home for a Game 6 and it's going to be exciting and a great challenge for us."
Stepan scored two goals after missing Game 4 with a broken jaw. He played with a plastic guard attached to his helmet to protect his injury. Kreider had a goal and three assists, Nash had a goal and an assist, and Ryan McDonagh had two assists.
The Canadiens never panicked or appeared rattled when the Rangers rallied in the second period.
"We showed our resilience," Pacioretty said.
They did so without Therrien using his timeout following Kreider's game-tying power-play goal at 14:12 of the second period, which came with Tomas Plekanec in the penalty box for embellishment. Therrien said he could sense "the attitude on the bench was good," and Canadiens defenseman Mike Weaver said the team was calm.
"The composure level that we had, and just the leadership we have in this locker room, nothing really needed to be said," Gallagher said. "We understood why it was happening. We weren't playing very good hockey. We got away from our game plan. We tried too many hope plays and it cost us. They took advantage of it. We just needed to get back to doing what made us successful earlier in the game."
Gallagher made perhaps the play of the night with his assist on Pacioretty's goal. Gallagher was falling as he made a spin-o-rama move to get himself away from Rangers defenseman Marc Staal on the left-wing half-wall, but managed to make a tape-to-tape backhand pass across the zone to Pacioretty, who scored 3:44 into the second period for a 3-1 lead.
Any potential third-period comeback by the Rangers was hindered with 9:39 remaining, when defenseman John Moore leveled Weise with an illegal hit. Weise's helmet popped off and he had to be held up by Montreal defenseman P.K. Subban.
Moore received a match penalty, which carries a five-minute penalty and an automatic suspension from further competition until Commissioner Gary Bettman rules on the issue, according to Rule 21 of the NHL Rulebook. Moore has a hearing scheduled for Wednesday with the NHL Department of Player Safety for an illegal check to the head.
Weise left briefly, but Therrien said he was cleared by the medical staff so he returned and finished the game.
"John is definitely not the type of player to try to hurt someone, but it was a late hit and it was the right call on the ice," Vigneault said.
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