New York won it after Pavel Dorofeyev tied it 4-4 for Vegas with 14 seconds remaining in regulation. With Carter Hart on the bench for the extra attacker, Dorofeyev picked up a loose puck below the right circle and scored past the outstretched glove of Ilya Sorokin.
The Golden Knights then had a chance to complete the comeback after Kyle MacLean was assessed a minor penalty for high-sticking with just four seconds remaining, but the Islanders were able to kill off the penalty in overtime.
Marc Gatcomb and Simon Holmstrom scored for the Islanders (17-11-3), who have won four of their past five games. Sorokin made 33 saves.
Mitch Marner had a goal and an assist, and Mark Stone and Jack Eichel each had two assists for the Golden Knights (14-6-9), who had their four-game winning streak end. Hart made 23 saves.
Noah Hanifin gave the Golden Knights a 1-0 lead at 12:02 of the first period during 4-on-4 play. Sorokin blockered aside Eichel’s initial shot from the top of the right circle, but the puck went right to Hanifin, who shot the rebound into the open net.
Marner extended the lead to 2-0 on a goal similar to Hanifin's at 16:01. Sorokin once again stopped Kaedan Korczak's initial shot, but Marner quickly buried the rebound past the goaltender's outstretched blocker from the left circle.
Horvat cut it to 2-1 during another 4-on-4 play at 19:33. Ryan Pulock fed Horvat for a one-timer that beat Hart short side from the right circle.
Gatcomb scored his first of the season to tie it 2-2 at 3:56 of the second period. Casey Cizikas skated around the net, turned, and sent a centering pass to Gatcomb, who chipped the puck over Hart's left pad from the edge of the crease.
Holmstrom gave the Islanders a 3-2 lead at 13:30. Calum Ritchie sprung Holmstrom down the left wing on a rush, and he beat Hart under his glove from the top of the left circle.
It was Holmstrom's first point since Nov. 8 (15 games).
Ivan Barbashev tied it 3-3 at 1:25 of the third period, diving in the low slot to chip a pass from Braeden Bowman over the left pad of Sorokin.
Horvat scored his second of the game on the power play to put New York back in front 4-3 at 10:15. He took a pass from Mathew Barzal and scored five-hole with a one-timer from the high slot.