The Canadiens managed to blow leads of 2-0 and 3-1.
Frans Nielsen tied the game with the only goal of the third period.
Then, after the Canadiens had some chances in the early part of OT, John Tavares started a three-way passing play that left defenceman Thomas Hickey wide open to Carey Price’s left for the goal that won a strange game.
It was the first goal of Hickey’s career.
The Islanders clicked on two of three power plays, both goals scored by Matt Moulson.
Max Pacioretty had two goals for the Canadiens, who got an early one from Travis Moen.
With the Canadiens nursing a 3-2 lead, Frans Nielsen scored halfway through the third period to set up OT.
The Canadiens outshot the visitors 33-25.
So for only the fourth time this season, the Bell Centre crowd goes home grumbling.