The Canadiens reached 90 points for the season and moved into seventh place in the Eastern Conference -- one point in front of the New York Rangers. Montreal has five games remaining and the Rangers just four.
The Islanders, mired in last place in the East, surrendered three power-play goals overall and fell behind 4-0 just 3:12 into the second period.
Yann Danis allowed all five goals on 38 shots.
Jaroslav Halak got the win by making 26 saves.
Alex Tanguay, Andrei Markov and Mike Komisarek also scored for Montreal, which has dramatically improved its playoff hopes by winning five times in six games.
The Islanders' goal came from Jeff Tambellini midway through the second period.