With the scored tied 2-2 midway through the final period, Alexei Emelin fired a shot from the high slot that Galchenyuk corralled at the right side of the net and directed past Martin Brodeur for the decisive score.
Rene Bourque added a goal and an assist, Max Pacioretty scored and David Desharnais provided two assists for the Habs, who improved to 6-0-1 in their last seven games.
Carey Price notched the win with 28 saves.
Brodeur finished with 14 saves.
2014: The Year in Music [PHOTOS]