Michael Cammalleri tallied the Habs' only regulation score and Montreal went on to clinch its fourth post-season appearance in four seasons.
Carey Price stopped 42 shots for Montreal, which holds the sixth seed in the Eastern Conference.
Chicago, which is tied with Anaheim for the seventh seed in the West, got its only marker from Patrick Kane.
Corey Crawford turned aside 32 shots as the Blackhawks lost their second straight game.
Celebrity Families of 2014 [PHOTOS]