The Canadiens pulled Price for an extra skater with 1:08 left, but couldn't get anything past Craig Anderson, who finished with 27 saves.
Anderson was solid in net all night as he matched a career high by winning his sixth straight start. He helped the Avalanche kill a late penalty and earlier thwarted a scoring attempt from Andrei Kostitsyn, lunging out of the net and knocking the puck off Kostitsyn's stick.
"We found a way," Anderson said. "It doesn't matter if it's 3-2 or 6-5, we're finding ways to win."
The only thing Anderson was displeased with was a late slashing penalty called on him at the end as his emotions -- unlike the puck -- got away from him.
"I apologized to the ref for taking that 2-minute slash. It was uncalled for," he said.
Anderson also picked up an assist on Wilson's goal in the first period on a simple dish to his defenseman.
"Sweet," Anderson said when informed of his assist. "We're getting things done on the power play and finding ways to score lots of goals. Tonight, we got three and it should be more than enough most nights. I gave my team a chance to win."
That's been happening quite a bit of late, the Avalanche turning in their longest winning streak since last January.
"We've got a good thing going," Avalanche coach Joe Sacco said. "The one thing we've got to guard against is not getting too high. We should be proud of the fact we've won six in a row, but we've got to keep on an even keel. I like the direction the team is going and the way we played tonight."
The Canadiens began their seven-game road swing on the wrong foot. But they're not looking too deeply into this loss.
"The anger and frustration lies in the fact that this group of guys expects to win hockey games," Cammalleri said.
The injury-riddled Avalanche are steadily mending as Paul Stastny returned to the lineup Sunday after missing a game with an upper back injury.
Galiardi's also regaining the strength in his wrist. He may not have a firm handshake yet, but his shot remains lethal.
And then there's always the chest bump.
"It feels great to come back and make an impact," said Galiardi, who missed 17 games with the injury. "That's what I tried to envision when I was out. We got two wins in my two games back so I'm pretty happy. There are a few things I still need to work on and getting the rust out a bit, but two wins is what we wanted."
This was the only meeting between the two teams in 2010-11. ... Avs F Ryan O'Reilly had two assists. ... The Avs announced before the game that D Kyle Quincey will need season-ending shoulder surgery. ... Colorado is 7-0-0 against Northeast Division teams in the last two seasons.
Copyright by STATS LLC and The Associated Press
DENVER - DECEMBER 19: Matt Duchene #9 of the Colorado Avalanche skates during the pre-game warmup before facing...