The 4-1 Avalanche got to the shootout with the help of two goals and an assist by David Jones. Paul Stastny and Kyle Quincey each notched a goal and an assist each for Colorado, which has won four in a row for the first time since a six-game streak last December.
Semyon Varlamov got the victory by stopping 38 of the 43 shots he faced.
The Canadiens' offense was led by Brian Gionta's goal and two assists. Max Pacioretty and David Desharnais added a goal and an assist apiece.
Carey Price stopped 25-of-30 shots in Montreal's second straight setback.