Alexei Ponikarovsky had two goals and two assists and Toronto took a four-goal lead before going on to beat Montreal 5-2 on Saturday night.
"It's always great to win when we play Montreal," said Grabovski, who was traded to the Maple Leafs by Canadiens GM Bob Gainey on July 3 and has no love lost for his former team. "I'm so excited and happy my line played well."
Toronto is 11th in the Eastern Conference with 73 points, eight behind eighth-place Montreal, and is likely to miss the playoffs for a fourth straight season.
The Canadiens, who remain one point ahead of ninth-place Florida, are 1-3-2 since Gainey stepped behind the bench after firing Guy Carbonneau on March 9.
"I didn't have much to say to the players after the game but (Sunday) we're going to meet with the players that didn't play well, those that I'm unhappy with the way they're playing," Gainey said.
A week earlier, Gainey had said that the team would need to improve on the three standing points it claimed through his first three games behind the bench. Montreal lost 5-4 in Ottawa on Thursday after losing 4-3 in a shootout against the New York Rangers two nights earlier.
"I think our next goal should be to win a game in 60 minutes," Gainey said. "We haven't won a 60-minute game in a long time and really our goal is to win a game where we play and we win the game and we deserve to win the game, not just based on a couple of power-play goals or on incredible goaltending but a team game where we get everybody participating in a way that we would resemble more what our competition looked like tonight."
The Maple Leafs led 4-0 following Ponikarovsky's second goal in 6 minutes 9:09 into the second period.
"The whole line was awesome tonight - skating, shooting, passing, doing everything that they can do - and it was great to see," Blake said.
Maxim Lapierre scored two straight goals 2:32 apart to draw Montreal to 4-2 at 15:22.
The Canadiens, booed by the sellout crowd of 21,273 moments earlier, came close to making it a one-goal game before the end of the period with a number of good scoring chances, particularly a deflection by Saku Koivu that struck the right post during a power play.
Martin Gerber stopped 26 shots for Toronto, which has won four of six.
Jaroslav Halak made 32 saves for Montreal, which lost its fifth in a row.
Kulemin came close to opening the scoring in the opening minutes before staking Toronto to a 1-0 lead with his 12th goal 7:51 in.
Grabovski made it 2-0 just 23 seconds later when he slipped a shot under Halak's pads from a sharp angle for his 18th goal at 8:14.
Ponikarovsky, who assisted on both goals, made it 3-0 with his 20th goal 3:09 into the second.
He added a power-play goal at 9:09 when he scored from the edge of the crease for his 21st goal that increased the lead to 4-0.
Lapierre, who ended up on the Maple Leafs' bench during a skirmish at the end of the first period, drew some life back into the crowd with his 13th goal at 12:50. The Candiens center drove the slot and redirected Chris Higgins' turnaround pass from the left side past Gerber and into the top right corner.
He got his 14th goal moments later when he beat Gerber at 15:22 to draw Montreal within 4-2.
After the Canadiens pressed for more late in the second, Blake gave Toronto a three-goal margin when he beat Halak with a wrist shot from the left side
Kulemin came close to scoring 1:29 in. Referee Mike Leggo's ruling that Halak was able to keep the puck from crossing the goal line was supported after a lengthy video review.
Notes: Grabovski and Kulemin each had career highs for points in a game. Ponikarovsky had a career-high five points - two goals and three assists - against the New York Rangers on Dec. 16, 2006. ... Canadiens RW Georges Laraque returned after missing seven games because of a back injury. ... RW Matt D'Agostini, LW Gregory Stewart and Ds Patrice Brisebois and Mathieu Dandenault were healthy scratches for Montreal.