Erik Cole scored two goals. including the go- 1, on Saturday at Rogers Arena.
Blake Geoffrion and P.K. Subban scored while Max Pacioretty added two assists and Carey Price made 32 saves for the Canadiens, who have won three of their last five contests.
The Canucks remain two points back of St. Louis, who topped Columbus, 4-1, earlier on Saturday, for the top spot in the overall NHL standings.