Elias Pettersson had a power-play goal to help Vancouver snap a four-game losing streak.
''There's a lot of adversity around our group,'' Canucks coach Travis Green said. ''We've talked about before the game, things are going tough, we're going through adversity. It shows a lot about the players as individuals, it shows a lot about the team and how you respond.''
''We talked about character and times like this reveal a lot about players and teams.''
After winning three of nine games against the Canadiens in last season's North Division, the Canucks picked up their first regulation win in Montreal since 2007.
''It felt great,'' Pettersson said about getting a win at Bell Centre. ''They didn't start their season that well either so both teams were fighting for points.''
Ryan Poehling scored for the fourth time in 10 games, and Jake Allen had 40 saves for the Canadiens oine day after Montreal fired general manager Marc Bergevin.
Canadiens president and CEO Geoff Molson had called coach Dominique Ducharme on Sunday to ask to speak with the players before holding a press conference Monday morning.
''It was obviously two emotional days,'' Ducharme said. ''We all worked with Marc on the day-to-day, 3 1/2 years for myself. He's someone I have a lot of respect for and a lot of our veterans lose someone that had the success and happiness of everyone at heart.''
Quinn Hughes set up Pettersson for a one-timer to open the scoring on the power play 8 minutes into the first period. It was Pettersson's fourth of the season. Hughes got his team-leading 14th assist and J.T. Miller his 13th and team-high 20th point.
Pettersson got his first goal since Nov. 9 and admitted that he struggled with confidence.
''I feel like everything is confidence,'' he said. ''It's a slow start for me personally. I've been having a tendency to overthink and kind of going away from hard work. Today, I was just thinking about working as hard as possible and it's definitely nice to get one on the power play too.''
Poehling levelled things at 1-1 with 1:21 left in the first. After starting the year in the AHL, Poehling is now tied with Nick Suzuki for goals by a Canadiens center with four.
Garland brought Vancouver back on top in the second period. Bo Horvat intercepted Josh Anderson's no-look pass along the boards and passed to Garland who scored his seventh - tying Miller for the team lead.
The Canadiens tried to mount a late comebackbut they were stopped in their tracks by the Canucks penalty kill and Demko's impressive play.
''I've been wanting to find some more key saves in my game in the last little bit,'' said Demko. ''I don't think my game's been bad but I think there's always room for improvement. It seems like we're losing by one goal every night so it was an important game for us today.
''You could feel right from the puck drop that it was going to be a tight game. There wasn't going to be much out there so every play was pretty important.''
With two power-play opportunities against the Canucks, the worst penalty-killing unit in the NHL, Montreal still couldn't find the back of the net with the man advantage.
Canucks: At Ottawa on Wednesday night to finish a five-game trip.
Canadiens: Host Colorado on Thursday night to wrap up a two-game homestand.
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