Matt Moulson scored twice and Frans Nielsen added a goal in the third period for Islanders (7-9-1), who came back twice from a pair of two-goal deficits to end a two-game slide and win for just the third time in 10 games.
Moen got things going just 49 seconds into the game when Colby Armstrong picked the pocket of Islanders defenceman Andy MacDonald behind the net before feeding Moen for his second of the season.
Pacioretty picked up his first of the night on the power play at 11:02 of the first period. David Desharnais, stationed to the left of the crease, moved a P.K. Subban pass along to Pacioretty at the inner hash marks of the right faceoff circle.
After going his first 10 games without a goal, Pacioretty now has four goals in three games.
The Canadiens outshot the Islanders 14-3 in the opening period, marking the third straight game they’ve held their opponent below five shots in the first 20 minutes. Montreal has also kept its opponents below 10 shots in first period of each game of their six-game winning streak.
The Islanders got one back early in the second on a power play of their own. Moulson deflected Mark Streit’s point shot for his eighth of the season 34 seconds into the period.
Pacioretty restored Montreal’s two-goal lead eight minutes later after a strong shift by his line. Working with Erik Cole behind the Islanders net, Desharnais found Pacioretty in the low slot at 8:30.
Moulson picked up his second of the night — again on the power play — at 16:57 of the second on a feed from John Tavares behind the Montreal net.
Grabner found Hickey alone to the left of Price for the game-winner at 3:12 in overtime.
Price stopped 21 shots for the Canadiens, while Evgeni Nabokov made 30 saves for the Islanders.
NOTES: The Canadiens allowed more than a goal against for the first time since Feb. 12 against Tampa Bay (a 4-3 shootout win) … Defencemen Tomas Kaberle and Yannick Weber were once again healthy scratches while rookie winger Brendan Gallagher missed his third straight game with a concussion … The Islanders, without injured defencemen Matt Carkner and Brian Strait, scratched blue-liner Radek Martinek and forwards Eric Boulton and David Ullstrom.