Patrik Elias and Jacob Josefson each tallied in the first period and Marek Zidlicky added two helpers for New Jersey, which has been eliminated from post-season contention.
Martin Brodeur made 19 saves in the victory.
The Canadiens cut their deficit to 3-1 when Max Pacioretty found the net 6 1/2 minutes into the third and Lars Eller scored with 21 seconds left, but Montreal could get no closer.
Carey Price turned aside 21 shots for the Habs, who came into the contest tied with Boston for the Northeast Division lead.
Celebrity Families of 2014 [PHOTOS]