Montreal (7-3-0) fell behind 2-0 midway through the second period before captain Nick Suzuki sparked the resurgence with a power-play goal that extended his point streak to nine games (two goals, 11 assists).
Juraj Slafkovsky followed with a power-play goal of his own early in the third before Mike Matheson scored at the 8:19 mark to give the Habs the lead.
Demidov added another tally, Alexandre Carrier contributed two assists, and goalie Jakub Dobes stopped 28 of the 31 shots he faced.
Elias Pettersson scored and had two assists and Conor Garland registered one of each for the Canucks (4-5-0).
Vancouver also got a goal from Jake DeBrusk, two assists from captain Quinn Hughes and 20 saves from Kevin Lankinen as the team dropped its third straight game.
Canucks: The home side took a 2-0 lead midway through the second period when DeBrusk tipped in a Quinn Hughes shot on the power play, but ran into penalty trouble midway through the frame and saw Montreal level the score and take the momentum.
Canadiens: With Patrik Laine expected to miss several months following surgery for a core injury, the Habs will need to look elsewhere for offence. Several players stepped up Saturday, with eight players netting a goal, an assist or both.
Slafkovsky levelled the score at 2-2 less than two minutes into the third period, firing a wrist shot in from the bottom of the faceoff circle on Montreal’s second man advantage of the night.
Garland collected his 300th NHL point with his goal 16:12 into the third period.
Canadiens: Visit the Kraken in Seattle on Tuesday.
Canucks: Host the Edmonton Oilers on Sunday.
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