Matt Moulson's goal in the fourth round of 3, at Nassau Coliseum.
After the teams traded goals in the first round and misses in the second and third, Moulson skated down the center of the ice and snapped a wrister past the stick side of Martin Biron.
The Rangers' John Mitchell had a chance to keep the shootout going, but his five-hole attempt was turned aside by Evgeni Nabokov to snap a two-game slide for the Islanders.
Moulson had a goal and an assist in regulation, while P.A. Parenteau scored twice for the Islanders, who improved to 8-8 in games played past regulation this season. Nabokov stopped 33-of-36 shots.