Juraj Slafkovsky had a goal and two assists, Ivan Demidov had three assists, and Noah Dobson, Mike Matheson and Oliver Kapanen scored for the Canadiens (26-14-6), who are 9-2-2 in their past 13 games. Nick Suzuki and Alexandre Texier each had two assists, and Jakub Dobes made 20 saves.
Montreal will begin a three-game road trip at the Washington Capitals on Tuesday. The Canadiens finished a four-game homestand 3-1-0 after going 4-1-2 on a seven-game road trip.
“Those two points were big for us," Carrier said. "We need them for the standings, obviously, but also to finish on a strong note at home."
Elias Pettersson, Evander Kane and Max Sasson scored for the Canucks (16-24-5), who are 0-5-2 during their losing streak. Nikita Tolopilo made 35 saves in his first game since Dec. 8.
“I think it was such a fast game for him, the pace, that there were a couple there that he might want back,” Vancouver coach Adam Foote said.
The 25-year-old goalie was recalled from Abbotsford of the American Hockey League on an emergency basis on Sunday after Thatcher Demko was placed on injured reserve.
“There’s no excuses,” Tolopilo said. “It wasn’t an easy game, but I need to get better. I’d probably like a couple of goals back. I think there were some really good things that I liked about my game, but some things where I want to clean up and get better. A couple of goals, like, I just want to look at again.”
Montreal scored three unanswered goals in the third period to take the lead.
Matheson made it 4-3 just 29 seconds into the third with a wrist shot from between the circles that went in off the right post.