Grabovski scored his first NHL goal, Patrice Brisebois and Steve Begin each scored his of the season, Alexei Kovalev got his second and Chris Higgins and Andrei Markov each got their third for Montreal (4-2-2), which stopped a four-game winning streak by Boston (5-3-0). Montreal won its second straight game at home.
Dennis Wideman got his first of the campaign on a third-period power play for Boston.
Cristobal Huet was stellar in the Montreal net as the Bruins had a 32-20 shot advantage, but Manny Fernandez, coming off a shutout win over the New York Rangers, had a weak outing for Boston.
Higgins got the scoring underway 12:14 into the game when he knocked in the rebound of a Mike Komisarek wrist shot.
Tomas Plekanec won a faceoff from Marc Savard back to Kovalev for a low shot that beat Fernandez at 6:28 of the middle frame. Then, Begin completed a two-on-one with Tom Kostopoulos at 17:48.
Brisebois moved in from the point to one-time in a Plekanec pass on a power play 1:45 into the third period.
Wideman's low shot from the high slot beat Huet at 6:61, but another two-on-one saw Grabovski fire Bryan Smolinski's pass into an open side at 9:34.
Markov was at a bad angle, but still lifted a high shot over Fernandez on a power play at 14:39.
The Bruins begin a three-game homestand Thursday night against Chicago, while Montreal next plays road games Friday in Carolina and Saturday in Pittsburgh.
Notes: Smolinski became the 220th NHL player to play 1,000 career games. Alexei Kovalev will play his 1,000th Friday night in Carolina. . . Andrei Kostitsyn was a healthy scratch for a second straight game along with Josh Gorges, while Garth Murray is out with a broken ankle. . . Brandan Bochenski, Bobby Allen and Jeremy Reich didn't play for Boston. . . Montreal boxer Lucian Bute was saluted before the game for winning the International Boxing Federation super-middleweight title.