Saku Koivu scored his 21st and 22nd goals of the season, a career high, for the Canadiens, who have won nine of their last 11 games as they battle for a playoff spot.
Montreal has won nine consecutive home games for the first time since 1981, when they did it in the midst of a 21-game home unbeaten streak.
Halak recorded his seventh win in the last eight games and his second shutout - both 1-0 against Boston - in that span. The first came in back-to-back wins over the Bruins March 20 and March 22.
And even though No. 1 goalie Cristobal Huet is due to return from a hamstring injury, Halak has staked a claim to the starting job during the playoff drive.
Koivu's first goal drew gasps from the crowd as he got between two forwards, split defencemen Zdeno Chara and Andrew Ference and went in alone to beat Hannu Toivonen with a deke to the forehand on a power play 16:46 into the game.
The Canadiens went on a two-man advantage for 1:40 to start the second period, but failed to score as Koivu rang a shot off the post from the edge of the crease.
The Canadiens' 100th consecutive sell-out audience of 21,273 had little else to cheer in a nervy, must-win game against a 35-39-6 Boston team already eliminated from the playoffs until Koivu scored again at 14:42 of the third.
The Canadiens captain went around Chara and slid in a backhand shot. He also tied his career high for points with 71, matching his 2002-03 totals.
Montreal ends the season on the road with games Thursday against the Rangers in New York and Saturday in Toronto.
Toivonen, called up from AHL Providence on Monday for late-season look by Bruins management, was mostly solid in goal, particularly during the two-man advantage, as well as when stopping Tomas Plekanec in alone in the second period.
Boston's recent call-up Petr Kalus, only the third player ever to score on his first three career NHL shots, was stopped on his fourth shot in the middle period.
Notes - With Toivonen in goal, Boston's Joey MacDonald didn't dress along with injured Chuck Kobasew and Jason York. . . Huet is cleared to return from hamstring surgery but won't be clear to play until Wednesday when he officially comes off the injured reserve list. . .Sergei Samsonov, Josh Gorges, Alexander Perezhogin and Garth Murray didn't dress.