The Thrashers also edged closer to making the playoffs for the first time in their seven-year history.
Marian Hossa, Atlanta's leading scorer, had a pair of assists as the Thrashers broke a tie with idle Tampa Bay for the Southeast lead with 82 points.
Atlanta's other goals came from Ilya Kovalchuk, Vyacheslav Kozlov, Eric Belanger and J.P. Vigier.
The Thrashers broke the game open in the second period, scoring four times in less than nine minutes for a 6-0 lead. Montreal, which is also fighting for a playoff spot, lost for the fourth straight time and 11th in 15 games.
The Thrashers took a 2-0 lead in the first period with Kovalchuk and Sim scoring three minutes apart to help Atlanta beat Montreal for the first time this season after three losses.
Kovalchuk, who has a goal in three straight games, got his 36th on a power play 9:45 into the period, blasting a slap shot from the left point past Montreal goaltender Jaroslav Halak, the puck dribbling into the net after first hitting the pads of Halak.
Sim scored his 16th goal at 11:45 when Belanger stole the puck and passed to Sim, who poked it past Halak.
Kozlov began the Thrashers' second-period onslaught with his 22nd goal at 3:41, then drawing an assist 30 seconds later on a goal by Belanger, his 14th.
When Vigier scored his fifth goal on a rebound at 6:47, it was 5-0 and the Canadiens changed goalies.
In came David Aebischer, who was beaten less than two minutes later when Sim knocked in a rebound at 8:43 for his 17th goal. Montreal scored at 9:27 on a goal by Guillaume Latendresse, his 12th, beating Atlanta goalie Kari Lehtonen, who has been outstanding during the five-game winning streak. He has allowed an average of less than two goals a game during the stretch.
The Canadiens scored at 8:24 of the third period on a goal by Radek Bonk, his 12th.
Both Montreal and Atlanta have 13 regular-season games remaining.
Notes: The Thrashers have won five games on three other occasions, the most recent was Dec. 19-27, 2006. ... Kozlov's assist on the second-period goal by Belanger was the 400th of his career. ... The Thrashers are 5-0 since acquiring forwards Keith Tkachuk and Pascal Dupuis and D Alexei Zhitnik.