Jaroslav Halak kept the puck out of the net while being peppered with 40 shots to record his fifth career shutout and first of the season.
Glen Metropolit also scored on the power-play for the Canadiens, who ended their five-game losing streak.
Martin Brion faced 28 shots in the New York goal. Jack Hillen had a team-high five shots on goal.
Markov, who had been sidelined by a lacerated ankle tendon suffered in the first game of the season, opened the scoring at 7:44 of the first period. Markov put the Habs ahead 2-0 at 13:12 of the second period.
The Islanders missed a solid chance to get back in the game on a 4-minute power play early in the third period while trailing 2-0.
Notable deaths of 2014 [PHOTOS]