The victory enabled the Islanders (5-7-1) to end a five-game losing streak, while the Rangers (7-6-1) were consigned to a first defeat in four contests.
The game was tied at 3-3 at the end of overtime before Frans Nielsen and John Tavares scored for the Islanders in the shootout while Marian Gaborik and Rick Nash both missed for the home team.
The Rangers made a flying start when they scored twice in the opening period, with Dan Girardi grabbing a first goal of the season and Gaborik celebrating his 31st birthday by putting his team 2-0 ahead.
However, the Islanders rallied to seize control in the second period, scoring three times in a seven-minute spell to surge ahead.
Colin McDonald netted 29 seconds into the period before Tavares made it 2-2 when he scored after the Islanders had killed off back-to-back penalties, including 33 seconds with a two-man disadvantage.
Brad Boyes then gave the Islanders the lead when he steered a wrist shot past Martin Biron, who made 28 saves.
"We responded in the second and we made some changes with our lines and I liked the way we responded and played well," Islanders coach Jack Capuano said.
The Blueshirts tied it at 3-3 in the final period when Carl Hagelin scored a powerplay goal that was confirmed on review, but were unable to find another way to get the puck past the Evgeni Nabokov, who stopped 36 shots.
"At least we get that one point," Hagelin said. "It was huge because we need every point we can get.
"But after that start and the way we played, we really should have had two points."
- Ice Hockey
- Sports & Recreation
- John Tavares
- Marian Gaborik