Montreal, which went 10-5-1 in March for its best month in 13 years, has a season-high six-game winning streak. The Canadiens, who host the Bruins again on Tuesday night, remained tied with New Jersey for sixth place in the Eastern Conference.
Huet made 32 saves for his seventh shutout of the season in 32 games. He trails only league leader Miikka Kiprusoff of Calgary, who had eight shutouts in 66 games through Friday.
"Right now he seems so stable and consistent in nets," said Canadiens coach and GM Bob Gainey, who answered "possibly" in French when he was asked in that language if Huet was going to start Tuesday.
"He probably makes eight to 10, 11, or 12 difficult saves," Gainey said, "but it's hard to pick them out when you go back on them because he's in position, he's in position early and he's making the stops."
Each of Huet's shutouts has come since Feb. 4, when he made 35 saves in a 2-0 win over the Bruins. The Frenchman stopped 28 shots in a 3-0 win in Boston on March 9. Montreal has won five of six against the Bruins this season.
"I like to play them, I guess," Huet said. "I think we played another great team game and we have a lot of success against them, but it's going to be another story on Tuesday."
Murray, who entered with a total of three goals in 46 career games, fought Bruins left wing Dan Lacouture 3:11 into the second and scored his fourth goal of the season later in the period, just moments after Boston goalie Tim Thomas made a spectacular stick save off Richard Zednik.
"It was great that we scored the first goal, and he got another one for that line so it made it a lot easier for us," said Zednik, who credited Thomas for making a great save.
Thomas stopped 33 shots, including three straight off Alexei Kovalev as Montreal had a 5-on-3 advantage for two minutes of the opening 2:33 of the third period.
"He got me last time when we were in Boston on a pretty good shot so it was my turn today," Thomas said.
The Bruins had three consecutive minors called, including penalties to rookie defensemen Mark Stuart and Andrew Alberts 23 seconds apart in the opening minute with veteran defenseman Hal Gill already in the penalty box.
Murray scored his fifth of the season -- second of the game -- 7:07 into the third, shortly after Huet made a huge save when Boston's Travis Green batted a puck out of the air.
"Nights like that don't happen too often for a guy like me," Murray said.
Montreal has outscored its opponents 18-5 while winning a season-high five straight at the Bell Centre. The Canadiens play five of their eight remaining games at home.
Right wing Glen Murray was sick and did not dress for Boston, which lost its sixth in seven. Glen Murray has three goals and three assists in a five-game points streak.
Huet made a right pad save on Bruins defenseman Brad Stuart's short-handed breakaway chance during Montreal's 4-on-3 advantage in the first.
Thomas caught a couple of huge breaks later in the period when Kovalev hit the post and Mike Ribeiro was unable to kick the rebound onto his stick for a shot at a wide open net. Kovalev got another scoring chance off the play but shot wide.
Chants of "Huet! Huet!" came from the sold-out crowd of 21,273 after the Canadiens' goalie made a fine glove save on defenseman Milan Jurcina's point shot on a Bruins power play late in the first.
Thomas was able to keep the game scoreless shortly before Garth Murray's opening goal when he stopped Andrei Markov's shot before lunging along the ice and using the paddle of his stick to swat away Zednik's shot at a seemingly wide open net.
- With D Nick Boynton lost to season-ending shoulder surgery, D Brian Leetch was also out of Boston's lineup. Leetch is day-to-day after he suffered a head injury in Wednesday's 4-3 loss in Buffalo. Leetch fell into an open bench doorway after he was high-sticked by Sabres C Daniel Briere, who was given a two-game suspension by the league the following day.
- Canadiens C Jan Bulis was a healthy scratch for the fourth time in five games, including each of the last three.
- Montreal has sold out each of its 36 home games.
- The Canadiens went 10-4-1 in January 1993 and went on to win their last Stanley Cup.