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.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Biologists detail four new deep-sea 'killer sponges'