Cole, Alex Galchenyuk and Lars Eller each scored in the middle period and added an assist each for the Eastern Conference-leading Canadiens, who improved to 6-0-1 in their last seven games.
Carey Price needed to make only 17 saves en route to his second shutout of the season and the 18th of his career.
Martin Biron yielded three goals on 18 shots for the Rangers, who lost their third straight and seventh consecutive in Montreal.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys