Moulson scored in the fourth round of the shootout and Nabokov then denied John Mitchell for the win as the Islanders beat the Rangers 4-3 on Friday night, moving them within six points of the last playoff berth in the East.
The Islanders were unable to hold 2-0 and 3-1 leads, but they won the tiebreaker when Moulson snapped a 10-footer past Martin Biron to start round four. Frans Nielsen of the Islanders and Marian Gaborik of the Rangers each scored in the opening round of the shootout, and neither team scored again until Moulson scored.
Nabokov, who returned after missing four games with the flu, stopped 33 shots through 65 minutes before improving to 7-0 in games decided after regulation.
"I felt it a little bit, but as the game went on I felt better," he said.
PA Parenteau scored twice and Moulson had a goal and an assist as the Islanders beat the Rangers for the second time in five tries this season -- but the fifth straight time in games that have gone beyond 60 minutes.
"Our guys really battled and Nabby played very well for us," Isles coach Jack Capuano. "He was competitive, he was aggressive in the net … he made some big saves for us down the stretch."
The Islanders (26-27-8) now have 60 points, six behind eighth-place Florida. They begin a four-game trip on Sunday against Ottawa.
"This is a crucial road trip for us," Capuano said.
Added Moulson: "This is the perfect kind of game to be in right now. It's good for our confidence. We needed a battle-type game like that to get going. We needed to win a close one. We have to know we can win those close ones going down the stretch. Hopefully we can feed off it and come out with the some compete level for this road trip."
The conference-leading Rangers (38-15-5), who got goals by Marc Staal, Gaborik and Derek Stepan, have 82 points, seven ahead of Boston in the Eastern Conference race and eight in front of second-place New Jersey in the Atlantic Division.
"I am happy we battled back and found a way to get a point," Rangers coach John Tortorella said, "but as far as where we are mentally in certain situations of the game at this time of the year, we need to be sharper."
The Rangers have dropped three of their last four, though they're still comfortably in first place in both the division and the conference as they prepare to host Buffalo on Saturday.
"It's a good place to be -- good to have teams gunning for you because you are on the top," said Biron, now 21-4-2 in his career against the Islanders." We talked about how good teams and good players play well when things are going good, and then play even better when fighting adversity. We need that desperation to stay where we are at."
After scoring just one goal in losses to Ottawa and Buffalo earlier this week, the Islanders doubled that total before the first period had reached the midway point.
Moulson gave the Islanders the lead at 6:07 when he set just outside the crease and snapped John Tavares' perfect passout behind Biron for his team-high 26th of the season. Parenteau, who signed with the Islanders in the summer of 2010 after the Rangers opted not to re-sign him, made it 2-0 at 8:42 when he sizzled a slapper from just inside the right circle past Biron's blocker.
"It was not the start we wanted," Rangers captain Ryan Callahan said. "After that, I thought we responded better."
The Rangers got one back with their first power-play goal in five games against the Isles this season. Staal snapped a shot from the left circle that beat Nabokov to the short side for his second of the season.
Parenteau's power-play backhander off a perfect cross-crease pass by Moulson at 8:11 of the second period restored the Islanders' two-goal lead. But Gaborik snuck past the defense, took Artem Anisimov's pass and beat Nabokov with a breakaway backhander at 11:49. Stepan tied it at 16:40 with a power-play goal on a shot that deflected into the net off Isles defenseman Travis Hamonic.
Hamonic was back in the lineup for the Islanders after missing two weeks with a broken nose and facial injuries. Rookie center Casey Czikas also made his NHL debut due to a back injury to Josh Bailey.
Rangers forward Ruslan Fedotenko returned after missing six games due to a suspected concussion after he was leveled by a hit from Tampa Bay's Dominic Moore on Feb. 9.
Material from team media was used in this report
1 - 0 NYI
2 - 0 NYI
2 - 1 NYI
3 - 1 NYI
3 - 2 NYI