Jake DeBrusk, Brad Marchand, Anders Bjork, Charlie Coyle and Danton Heinen also scored for the Bruins (16-3-5), who have won four straight and made quick work of their rivals, racing to a 3-1 lead after the first period that grew to 6-1 by the end of the second.
"This is probably the rink that we love to silence the most. We're not going to say the game's over by any means," Marchand told NESN at the end of the second. "Anything could happen. We've seen that already this year. But it's a lot more fun when this rink is quiet, you know, because they're very loud and obnoxious. So it does feel good to silence them."
Mission accomplished, though it was not without effort from the Montreal side. In fact, the Canadiens outshot Boston 37-24, but Bruins backup Jaroslav Halak made 36 saves and improved to 6-0-0 against Carey Price, his former teammate in Montreal.
Captain Shea Weber scored the only goal for the Canadiens (11-8-5), who have lost five straight.
Price gave up five goals on 11 shots before being pulled in the second period. Keith Kinkaid stopped 10 of 13 shots in relief.
Boston extended its points streak to eight games (5-0-3) and moved ahead of Washington atop the conference standings.
Claude Julien made no changes to a Canadiens team that blew a four-goal lead and lost 6-5 to the New York Rangers on Saturday.
Price gave up six goals on 34 shots to the Rangers and struggled even more against the Bruins, who were without Patrice Bergeron (lower-body injury).
A nice give-and-go led to DeBrusk's opener on the power play at 8:03 of the first period. Weber tied the game at 12:41 on a rebound at the side of the net.
That's when Pastrnak got to work on his seventh career hat trick. The NHL's leading goal scorer, Pastrnak beat Price with a one-timer on the power play at 14:24 for Boston's second score on five shots.
Marchand made it 3-1 on a bad giveaway by Jeff Petry behind his own net with 37 seconds remaining in the first. It was the winger's 600th NHL point. Price conceded three goals on eight shots in the first.
Pastrnak's goal eight seconds into the second period sealed Montreal's fate, and Bjork gave Boston a 5-1 lead on a breakaway a minute later.
Julien took a timeout and pulled Price, marking the first time that had happened since Dec. 9, 2017.
Pastrnak completed his hat trick when he deflected Brandon Carlo's shot past Kinkaid at 9:06 of the second. Pastrnak has 23 goals in 24 games this season.
Coyle made it 7-1 on a one-timer at 8:26 of the third as fans left Bell Centre. Heinen added an eighth for Boston with 2:02 left.