Bailey came down the left side and after a bit of stickhandling put a quick wrist shot past the stick side of Peter Budaj for the game-winner.
Frans Nielsen and Mark Streit found the net in regulation for the Islanders, who broke a five-game losing streak.
Al Montoya turned aside 28 shots to earn the victory.
The Canadiens got goals from Louis LeBlanc and Aaron Palushaj, but it wasn't enough to prevent their third loss in four games.
Budaj finished with 36 saves.