Carey Price made 34 saves to lift the Canadiens to a 3-1 victory Sunday night, giving Montreal wins in all four meetings this season.
"There's been a lot of matchups between those two teams in the past here, in the playoffs also," Canadiens coach Michel Therrien said. "But who knows what's going to happen? We don't know, but definitely, it brings some confidence. But honestly, there's still a lot of hockey to be played, and we're still a long way from the playoffs."
Dale Weise and Max Pacioretty each had a goal and an assist for the Canadiens, who completed their first regular-season sweep of Boston since taking all eight meetings in 2007-08.
"This win means a lot," Weise said. "That's a good hockey team over there, so it says a lot about our team. Price made some unbelievable saves to keep us in the game like he does every night, so it gives us a lot of confidence beating a team like that."
Price has won seven of eight and allowed 11 goals in that span. He extended his shutout streak against Boston to 159:25 until David Pastrnak scored with 4:31 remaining.
"In order to beat this team, our best players have to be our best players and we didn't have that tonight," Bruins coach Claude Julien said. "I don't think we made Price's night real hard."
Pastrnak cut Montreal's lead to 2-1 when he batted the puck toward the net and Price appeared to have made the stop, but his glove was behind the goal line and after replay, the goal was allowed.
Boston has one win in its last 11 games against the Canadiens, including six straight home losses.
"As soon as we start trying to play like them, we turn the puck over and that's where they capitalize," Bruins forward Brad Marchand said.
Weise gave Montreal a 1-0 lead 38 seconds into the second period when he converted a cross-ice pass from Pacioretty and beat Tuukka Rask.
Rask made 31 saves, but dropped to 3-13-3 against Montreal for his career.
Pacioretty scored on a breakaway 56 seconds into the third period when Weise fed him the puck after Zdeno Chara collided with Dougie Hamilton for a 2-0 lead.
Andrei Markov added an empty-net goal with 31 seconds remaining to cap the scoring for Montreal.
The Bruins had no power plays for the third time this season and are six points ahead of Florida for the final playoff spot in the Eastern Conference.
NOTES: Bruins backup goalie Malcolm Subban missed an opportunity to make his NHL debut against his brother, Canadiens defenceman P.K. Subban. ... Boston suffered its second regulation loss at home in its last 13 games. ... David Krejci has one goal in his last 15 games, while Chara has one goal since Oct. 21. for the Bruins. ... Weise has three goals in his last two games. ... Montreal outscored Boston 16-6 in the season series.