Backup goalie Justin Peters stopped all seven shots he faced before being replaced by Braden Holtby midway through the second period. Holtby made 11 saves for the combined shutout.
Brooks Laich added an empty-net goal in the final minute.
Carey Price made 29 saves for Montreal in his first full game of the preseason.
The game was sloppy, with 12 minor penalties called - including each team being whistled for too many men on the ice in the first period.