Glen Metropolit scored Montreal's final goal late in the third, and former Islander Marc-Andre Bergeron picked up two assists to help Montreal (16-18-3) snap a five-game losing streak and start a seven-game trip with momentum.
Martin Biron countered with 25 saves, but the reeling Islanders (13-16-7) still lost for the sixth time in eight games. New York's power play finished 0-for-6.
Halak (7-5) continued his season-long mastery over New York. Three of his seven wins have come at the Islanders' expense.
Markov needed exactly 7:44 to shrug off the rust after missing 35 games, converting Montreal's first power-play chance off a scramble in front.
Markov returned to action after lacerated tendons in his left foot kept him out since the season opener. The All-Star defenseman moved well enough in his return to capitalize on Islanders defenseman Jack Hillen's holding penalty, marking Montreal's first power-play goal in three games.
Halak made 14 saves in the opening period to maintain the lead, stopping Richard Park on a short-handed breakaway before smothering Nate Thompson's close-range wrist shot off a defensive zone turnover.
Biron made a diving stick save on Max Pacioretty's point-blank left post shot almost 4 minutes into the second to keep it close.
But Markov extended the Canadiens' edge with the man advantage when he fired a laser from the top of the left circle 13:12 into the second.
Bergeron passed it off to Markov after his point shot was blocked. Markov then beat Biron on the glove-side for his first multigoal game since Dec. 18, 2007, when he had a pair against Florida.
Travis Moen's high-sticking double-minor just 36 seconds into the final period put New York in position to make a run. The Islanders fired six shots in 4 minutes yet came up empty. Halak made 14 saves in the third, and Metropolit banged home Scott Gomez's one-time pass 14 minutes into the third for the insurance marker.
A heavy snowstorm helped to limit attendance to 7,842, though loud "Go Habs Go!" chants emanated from the Nassau Coliseum seats as Montreal fans heavily outnumbered Islanders fans.
New York couldn't silence the road fans and has been outscored 15-3 in its last three home games.
Biron is winless in his last six starts and has not posted a victory since Nov. 13 against Carolina.
Notes
Islanders D Bruno Gervais was back in the lineup after being benched in the club's previous two games against the New York Rangers. LW Jeff Tambellini was a healthy scratch for a fifth straight game. … Markov paired with D Jaroslav Spacek on the blue line and logged 20:24 of ice time.