The Canadiens started fast and then stymied the Bruins, winners of the Presidents' Trophy for the best regular-season record, to advance to the Eastern Conference final against the New York Rangers.
"It's definitely a special team and if we didn't know it before the playoffs, we definitely know it now," said Pacioretty.
Dale Weise and Daniel Briere, with a late power-play goal, also scored for Montreal.
Jarome Iginla's goal, which cut the Canadiens' lead to 2-1 with 2:08 remaining in the second, set the scene for a dramatic third period. The black and gold faithful hoped for yet another Bruins comeback.
Check out some photos from the game:
They almost got their wish early in the third when Iginla, pouncing on a rare Price rebound, hit the post. Boston came on but the Canadiens held fast and Price, improving his record in elimination games in 2014 to 5-0 including the Olympics, was rock-solid with a disciplined team defending in front of him.
The late Boston surge was not helped by a Johnny Boychuk penalty for interference with 4:31 remaining. Montreal scored on the ensuing power play when Briere's centring pass bounced in off Zdeno Chara's skate at 18:07 to pad the lead to 3-1.
Montreal killed off a late interference penalty to Andrei Markov — and a 6-on-4 Boston opportunity — to seal the win.
"Respect, you've got to earn it and I think tonight those guys earned it," said Canadiens coach Michel Therrien.
The Bruins outshot Montreal 30-18.
The game drew two sellouts: 17,565 at TD Garden and some 21,000 at the Bell Centre, where fans paid $10 to watch the game on the video scoreboard with proceeds going to charity.
They saw a contest in which both teams seemed at times weighed down by the occasion early on, knowing there could be an entire off-season to ponder a costly mistake.
The Canadiens finished the regular season 17 points and eight places below the Bruins. But speedy Montreal, which had five wins and five losses in the 10 previous regular-season and playoff games in 2013-14 between the two, proved to be a handful all year for Boston.
Yet the series was like rolling a boulder uphill for the Bruins, who rarely got their game going against Montreal. Boston coach Claude Julien had said Game 7s deserved your best. The Bruins failed to deliver for much of the night.
The series has been a roller-coaster ride with no shortage of subplots, most of which involved P.K. Subban whose star continues to grow. When he wasn't firing bullets from the blue-line or skating circles, the flamboyant Canadiens defenceman was dodging water aimed his way from the Boston bench and dealing with racism on social media.
Subban embraced the attention and found himself in the spotlight again ahead of Game 7 when he pointed to the crowd, noise and energy in Boston's TD Garden before saying: "I can't wait to take that all away from them."
Therrien refused to talk about any issues with the Bruins after the Game 7 victory.
"I'm not going to talk about the other team," said Therrien. "I never talk about the other team. One thing I could tell you we were a group that was really really motivated to win this series.
Subban focused on the task at hand Wednesday, forgoing the flash.
In a series where the team scoring the first goal had won all six previous outings, a fast start was mandatory. Especially when teams scoring first in Game 7s were 112-40 (.737).
Advantage Montreal as the visitors went ahead on their first shot, thanks to the fourth line, at 2:18 after Tuukka Rask kicked out what looked like an innocent long shoot-in. But Brandon Prust retrieved the puck and found Briere who sent a pass through Matt Bartkowski and Daniel Paille in front. Weise swept it in from Rask's doorstep.
Boychuk and Gregory Campbell both tried to hit Prust on the play, opening space for others.
The Bruins soon grew frustrated at the officiating, with first-period penalties to Brad Marchand (goalie interference) and Chara (holding). Boston killed them off but looked disjointed and a little desperate at times, trying to force passes.
The Bruins finally started throwing their weight around at the end of the period and had a gilt-edged charge after Patrice Bergeron stole the puck off a Canadiens defenceman. But Brad Marchand fired high from point-blank range. Price then had to stop a Carl Soderberg redirect.
Boston outshot Montreal 9-6 after 20 minutes but had nothing to show for it.
The second period started poorly for Boston with Marchand sent to the penalty box for unsportsmanlike conduct for a snow shower aimed at Price. That call prompted garbage thrown from the stands.
Boston dug itself out of that hole and looked to fight back. Price waited out Bergeron as he drove at the goal, trying to get the goalie to commit.
The Bruins outshot Montreal 7-1 at the start of the second period.
But it was the Canadiens who scored at 10:22 after Boston failed to clear its zone. A diving Brandon Gallagher somehow found five-foot-seven David Desharnais, who emerged with the puck after Loui Eriksson, Soderberg and Bergeron failed to deal with it. Desharnais headed towards goal but rather than shooting, sent a no-look pass to Pacioretty to his right. The Montreal sniper rifled a shot into the goal before Rask could slide to the other side of the crease.
Desharnais, under fire for his sub-par performance for much of the series, had a whale of game.
Boston finally beat Price on the power play on an Iginla tip of a Torey Krug shot at 17:58. The goal, which came with seven seconds left in a Pacioretty penalty, ended Price's shutout streak of 103 minutes 46 seconds.
The series was the 34th between the Bruins and Canadiens and marked the ninth time — a record in North American pro sports — that a Game 7 was required. Montreal held a 5-3 advantage in the eight prior Game 7s, but the teams had split the six such deciders in Boston.
The Bruins had the last laugh last time out, with Nathan Horton scoring at 5:43 of overtime to give Boston a 4-3 victory in the 2011 Eastern Conference quarter-finals. Boston went on to win the Stanley Cup.
Montreal held a 24-9 advantage in the playoff meetings between the two but Boston had won six of the last nine.
NOTES — It was the 11th Game 7 for Boston captain Zdeno Chara, passing Martin Brodeur, Andrew Ference and Scott Gomez (10) for the most among active players. And it was the 10th for Boston coach Claude Julien ... Wednesday's game came one year and one day after the Bruins' rallied from 3-1 down in the third period to dispatch the Maple Leafs 5-4 in OT in Game 7 in their first-round playoff series.
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