Rask stoned Max Pacioretty and Alex Galchenyuk on first period breakaways and went on to help the Bruins stretch their winning streak to six games with a 4-1 victory over the Canadiens on Wednesday night.
His 35-save effort was only his third win in 15 career games against Montreal.
"They had a couple of breakaways, but we kept it on the outside pretty good," said Rask, who ended Boston's five-game losing run against the Canadiens dating to last season.
After weathering an all-out Montreal attack in the opening period, Carl Soderberg, Patrice Bergeron and Milan Lucic scored in the second as Boston capitalized on every Montreal mistake.
Zdeno Chara also scored as the Bruins (43-17-5) improved to 9-1-2 in their last dozen games and extended a run without a regulation loss on the road to 11 games.
"He's been great all year," winger Brad Marchand, who had two assists, said of Rask. "He's the guy we look to be big for us.
"We didn't worry about anything that's happened in the past. It's more about how we've been playing lately. We focused on how we have to play."
With 91 points, the Bruins moved to within one point of idle Pittsburgh for the Eastern Conference lead. They return to Boston to face the Phoenix Coyotes on Thursday night.
"We're in this building and they come at us with a full court press," said Lucic. "Tuukka kept us in there.
"Whenever we can withstand that pressure it gives us a chance to win. We did that and we were able to get a few good shifts in at the end of the first that carried over into the second period."
David Desharnais replied for Montreal (35-25-7), which has lost three in a row and is 3-4-1 without injured No. 1 goalie Carey Price since the Olympic break.
Montreal outshot Boston 36-32.
As dominant as the Bruins have been, they often struggle against the Canadiens and it showed in the first period as Montreal held a 13-6 shot advantage.
"We felt good about how we pushed the play in the first period and we wanted to play the same way," said coach Michel Therrien. "Obviously, after their first goal, we have to respond better."
Only 1:33 into the second frame, rookie Jarred Tinordi misplayed a puck off a faceoff and Soderberg was alone in front to score.
Boston went on a counterattack after Andrei Markov fell and Bergeron finished off a give-and-go with Marchand at 9:25.
Lucic bumped Alexei Emelin off the puck and then trailed in on a rush to score on a routine shot that got between Peter Budaj's pads for his 20th of the season at 18:32.
Chara got another only 23 seconds into the third when he broke in from the point and put in his own rebound.
Montreal finally got one as Desharnais found the puck in a scramble with newcomer Thomas Vanek tying up traffic in the crease.
It was Vanek's first point in three games since he was acquired in a NHL trade deadline deal last week. And it was Montreal's first goal in seven periods since a 3-1 loss in Phoenix last Thursday.
Therrien tweaked his lines in the third period, notably moving Vanek to the first line with Pacioretty, and will consider changes to help his team find the net.
"I'm trying to find a solution to scoring," he said. "We're creating chances, but we can't finish right now."
The surprise number of the night was 24:03. That was the ice time of Montreal defenceman Francis Bouillon, which led all players both teams. Bouillon, replacing injured Josh Gorges, was dressed for the first time since the Olympic break and had been a healthy scratch for eight games. He finished even in plus-minus.
Notes: Galchenyuk played his 100th NHL game... Francis Bouillon was back in the Montreal lineup for the first time since Feb. 8, bumping Mike Weaver. Brandon Prust returned after missing seven games with an upper body injury. . . George Parros, Dale Weise and Rene Bourque were scratched. . . Boston sat Dougie Hamilton for a second game to make room for newcomer Andrej Mezsaros. Daniel Paille (concussion), Adam McQuaid (leg) and Dennis Seidenberg (torn ACL-MCL) are sidelined.