The Canadiens bounced back from deficits of 1-0 and 2-1 to take control of the game in the third period.
Thomas Vanek scored three times and was named the game's First Star.
Fourth-liners Travis Moen, Brandon Prust and Dale Weise (with en empty-netter) also scored.
The brilliant Nathan MacKinnon, Max Talbot and Jamie McGinn scored for Colorado.
Bonus: Leafs lost to Detroit.
The Canadiens scored three in 5:15 to win a tough one.
Brandon Prust scored to give the Canadiens a 3-2 lead early in the period, but Jamie McGinn took advantage of atrocious coverage to tie it up.
Then Thomas Vanek took over.
Two power-play goals to complete his hat trick, and raise his season total to 24.
Dale Weise's empty-netter, on an unselfish pass by Tomas Plekanec, sealed the deal.
Canadiens outshot Colorado 36-28.
Vanek finally scores
Thomas Vanek's 22nd – and first in blue-blanc-rouge – got the Canadiens back in the game at 1-1.
The celebration didn't last long. Maxim Talbot cashed a nice feed by Matt Duchene to restore Colorado's lead.
But Travis Moen, of all people, scored his second goal of the season – a backhander, while losing his balance – to tie it up.
Patrick Roy wasn't thrilled with J.S. Giguere on the Moen goal.
Canadiens outshot Colorado 14-13 in the period.
Is he really just 18?
The only goal of the game was a beauty ... if you're a Nathan MacKinnon fan.
The talented teenager shimmied and shook to maintain possession in the Canadiens end, then found himself alone in front of the net, whence he beat Carey Price with a backhander.
The Canadiens' power-play continues to fizzle.
And Colorado outhit the home team 14-7.
Shots were 8-8.
St. Patrick returns
Figure there might be a $ with a few digits beside it on the whiteboard in Colorado's dressing room Tuesday night?
Patrick Roy is back in Montreal for the first time as coach of the Avalanche.
And you can bet his players will have a bit of added financial incentive.
Roy was coy about the dollar figure during his lively appearance on L'Antichambre Monday night.
The rookie coach did, however, promise an entertaining game between his Avs and your Canadiens.
"We won't play defensive hockey," Roy promised.
Why should they? The Colorado lineup includes a bevy of young players who can skate and score – plus an aggressive D led by Erik Johnson, who's finally living up to his status as the first overall draft pick in 2006.
In the teams' previous meeting this season, Colorado won 4-1 in Denver. Peter Budaj got the start in that game, but Carey Price will gets a chance to beat one of his goaltending idols Tuesday night.