The Islanders reduced their deficit to one goal on three separate occasions, but could never get the score tied against Carey Price, who stopped 18-of-21 shots.
Montreal won its third in a row and its 13 points gives it a share of the early lead in the Eastern Conference with Tampa Bay.
Montreal had a 3-1 cushion heading into the final period, but John Tavares brought the Islanders within one just 13 seconds into the stanza with his sixth goal of the season.
Halpern restored a two-goal cushion 6:56 into the period, after which Doug Weight again cut the New York deficit to one by tipping in a shot with 7:04 remaining.
Andre Kostitsyn clinched it with an empty-net goal with 1:02 left.
Dwayne Roloson made 30 saves to take the loss. The teams will meet again Friday on New York's home ice.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut