Penalties whistled on Brandon Dubinsky and Mike Sauer less than 2 minutes apart in the initial frame each resulted in a Canadiens score, providing the difference in the contest.
Carey Price, meanwhile, withstood a furious Rangers attack in the third period, making 20 of his 31 saves in the final 20 minutes. He back stopped the Habs to their fourth win in five games.
Andrei Kostitsyn also scored and James Wisniewski added a pair of assists for New York.
The Rangers got tallies from Brian Boyle and Mats Zuccarello.