Kirby Dach and Juraj Slafkovsky each had a goal and an assist, and Jakub Dobes made 26 saves for the Canadiens (30-17-7), who have won two straight.
Lane Hutson, Zachary Bolduc, Oliver Kapanen and Ivan Demidov each had two assists.
Brock Nelson, Joel Kiviranta and Ross Colton scored for the Avalanche (35-8-9), who have lost six of their past eight games (2-4-2), including 5-2 at the Ottawa Senators on Wednesday. Scott Wedgewood made 21 saves.
Dobson put the Canadiens up 1-0 just 56 seconds into the first period following a face-off win by Kapanen. Slafkovsky collected the puck in the right face-off circle and knocked it back to Hutson. Hutson then fed a pass to Dobson, who buried a one-timer to the blocker side from the left circle.
Nelson tied it 1-1 at 4:09, skating into the offensive zone and beating Dobes' glove with a long-distance wrist shot.
Suzuki put Montreal ahead 2-1 with a power-play goal at 5:51. Demidov took a wrist shot from the right circle and Suzuki put the rebound past Wedgewood from in front.
Suzuki scored his second on a short-handed breakaway at 7:33. He chased down Kapanen’s long backhand flip pass up the middle, skated in alone and slid a backhander under Wedgewood’s stick.
Jake Evans increased the lead to 4-1 at 16:36 of the second period, stealing the puck away from Wedgewood behind the net and scoring on a wraparound.
Dach extended it to 5-1 just 40 seconds later at 17:16, putting the puck off Colorado defenseman Josh Manson that then squeaked through Wedgewood at the left post.
Kiviranta cut the deficit to 5-2 at 18:06 when he slid a rebound off a Sam Malinski shot past a lunging Dobes from the left circle.
Colton brought the Avalanche to within 5-3 at 4:38 of the third period. Valeri Nichushkin threw the puck to the slot from behind the goal line and Colton tapped it in at the top of the crease.
Alexandre Carrier collected a pass from Suzuki on a 2-on-1 and lifted a snap shot from the left circle to make it 6-3 at 5:45.
Kapanen threw the puck off Colorado defenseman Keaton Middleton and it slid to Slafkovsky at the right post, where he scored at 9:55 for the 7-3 final.
