Islanders forward Josh Bailey tied the game with 1:09 remaining in the third period when his shot from the right face-off circle appeared to have been saved by Robin Lehner, but play was stopped with 34.3 seconds remaining for video review, which determined the puck did cross the goal line to make it 2-2.
"I knew it had a chance," Bailey said. "I wasn't quite sure; from my angle, I could see his glove snap back a little bit. Obviously I would have rather seen it hit the mesh the first go-around. Your heart breaks pretty quick in those situations, but all in all, obviously it worked out."
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The goal extended Bailey's point streak to nine games. He and John Tavares assisted on Barzal's goal; Tavares has an eight-game point streak.
"Correct me if I'm wrong, but when that horn goes, that means [the NHL in] Toronto is saying that's a goal," Islanders coach Doug Weight said of Bailey's goal. "They don't want injuries, they want to stop the game as soon as possible. We dumped it in and got the puck back. I would have had a real problem with blowing the horn and saying inconclusive, and now we have a 50-50 puck and a face-off.
"I thought right when I heard the horn that it was a goal."
Barzal scored his first NHL overtime goal when he beat Lehner with a wrist shot from the slot for his 13th goal of the season and second game-winner in a row. He had his first NHL hat trick in a 5-2 win against the Winnipeg Jets on Dec. 23.
Jason Chimera scored for the Islanders (20-13-4), and Jaroslav Halak made 35 saves. New York trails the Washington Capitals by two points for third place in the Metropolitan Division.