John Tavares, Colin McDonald and Matt Martin each provided a goal and an assist for the Islanders, who handed the Canadiens their first regulation loss in 11 games.
New York rallied after blowing a two-goal lead and improved to 2-2-1 on a seven-game homestand.
Evgeni Nabokov turned aside 29-of-32 shots to earn the win.
P.K. Subban notched a goal and an assist while Michael Ryder provided three helpers for the Habs, who came into the contest on an 8-0-3 streak.
Carey Price surrendered five goals on 23 shots in the setback.
2014: The Year in Music [PHOTOS]