Ryan Getzlaf sent the game to overtime when he scored with one minute remaining in the third period. Cam Fowler had a goal and Gibson made 27 saves for the Ducks, who are still seeking their first win of the season (0-2-1).
"Obviously we didn't get the end result we wanted, but we got away with a point there," Getzlaf said. "I was proud of the way our guys came back and played that second and third period."
Nelson scored his second goal in three games to give the Islanders a 1-0 lead 7:47 into the game. Shortly after New York failed to convert on a power play, Nelson collected Jason Chimera's pass in the slot, turned and beat Gibson with a forehand shot. It was Chimera's first point with the Islanders.
Tavares made it 2-0 with 12:01 remaining for his first point of the season. With the teams at even strength, Cal Clutterbuck's stick broke as he attempted to shoot from the slot, but he followed the play and managed to kick the puck to Tavares with his left skate, and the Islanders captain beat Gibson on the forehand.
"We stayed with it," Tavares said. "We obviously don't want to give up a lead, but you've got to win that way sometimes. It happens. Great goal by Josh."
But Fowler got the Ducks back within one less than a minute later when his wrist shot from the point squeaked between Halak's pads to make it 2-1. It was Fowler's second goal in three games.