Nielsen scored in the first round, while all three Panthers shooters missed against Nabokov.
"I just tried to fake a shot a little bit and go to my backhand," Nielsen said. "I think he read me pretty good, but I was lucky to get it up and hit the post and the crossbar and went in. I was a little lucky, but I'll take it."
The Islanders missed a chance to win with about a minute left in overtime. Michael Grabner had an open net but his shot hit the stick of Florida's Ed Jovanovski.
The Islanders won for just the third time in nine games.
"You still want to win hockey games and play hard, keep building," Nielsen said. "We can't just lay down and die. We have to keep playing."
Florida is three points ahead of Washington for the Southeast Division lead. Washington beat Minnesota 3-0 on Sunday.
They picked up a point in each of the past two losses because the games went to overtime.
"Obviously, you want to win every home game but it was tough playing against loose teams like Edmonton and the Islanders are," Fleischmann said. "It's the end of the season and we are a kind of a tight group right now. Washington is coming after us for the playoffs. It's a fight right now."
The Panthers have lost three straight after a five-game winning streak and are 5-10 in shootouts this season.
"Unfortunately for us, the shootout has been a little bit of a stickler for us this year," Panthers coach Kevin Dineen said. "Right now, when things don't always fall on our side, there's a little tightness when it comes to the shootout."
The Islanders trailed twice in the game before they came back to win it.
"Our game plan doesn't change and that's the way we have to continue to play," Islanders coach Jack Capuano said. "I thought we did a good job of tracking and in all areas. They played well enough to win, too. Our goalie made some big saves in key times."
The Islanders tied it 2 at 12:22 of the third when Okposo scored while attempting to pass the puck. His pass from the top of the right circle was intended for Mark Streit, but it glanced off the stick of Florida's Dmitry Kulikov and into the net.
Florida went ahead 2-1 on Fleischmann's goal at 9:51 of the third. Streit attempted to bring the puck out from behind his own net but it hit the back of an Islander's player along the boards above the right circle. Fleischmann grabbed the loose puck and his shot from the right circle got past Nabokov. Fleischmann leads the Panthers with 56 points.
The Islanders tied it at 1 on Moulson's power-play goal late in the second. John Tavares passed the puck from the bottom of the left circle back to Moulson in the slot. He fired the puck past Theodore at 18:57, his team-leading 34th goal of the season.
The Panthers opened the scoring on Weiss' goal in the first, his 19th of the season. Tomas Fleischmann passed the puck from behind the Islanders' net to Weiss in front. His slap shot beat Nabokov at 5:55.
Islanders forward Moulson has 14 points in his past 14 games. ... Islanders C Tavares has 12 points in his past eight games. ... The Panthers wore their alternate two-toned blue jerseys for the last time Sunday.
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SUNRISE, FL - MARCH 25: Wojtek Wolski #8 of the Florida Panthers takes a shot on Goaltender Evgeni Nabokov #20 of...
(Photo by Eliot J. Schechter/NHLI via Getty Images)