SUNRISE, Fla. — The unlikeliest hero emerged deep into the second overtime early Saturday morning, and now the Islanders can close out this series on home ice.

Alan Quine’s one-timer beat Roberto Luongo at 16:00 of the second overtime to give the Islanders a 2-1 win in Game 5 and a 3-2 series lead over the Panthers, who could not convert a penalty shot in the first overtime.

“When you’ve got guys like him scoring big goals for us, it’s a great feeling,” said Calvin de Haan, who grabbed a bouncing puck while standing at the top of his own crease and threw it out of danger at 7:19 of the first OT, drawing the rare penalty shot call.

The Panthers’ Aleksander Barkov skated down on Thomas Greiss and could not get a backhand past the goaltender. Greiss made 47 saves, none bigger than that one.

“It definitely gives you a little boost when he stops that,” Frans Nielsen said. “He was huge tonight. There were big saves all night.”

The Islanders had a noticeably better first period than in any of the first four games, taking their first 1-0 lead of the series on Nielsen’s goal at 13:31 of the first.

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They still led 1-0 after two periods, but Barkov beat Greiss at 1:51 of the third to tie it. The goal was upheld after a coach’s challenge for offside. Replays showed Vincent Trocheck’s back skate could have been off the ice as Florida crossed the blue line, but it was ruled inconclusive and the goal stood.

The Islanders steadied themselves during the rest of the third and went to OT for the second time in the last three games of the series, again in a situation in which the overtime winner would put one of the teams in solid position.

Greiss was sharp in the first 10 minutes of the opening overtime, making five early saves even before de Haan was called for covering the puck in the crease — something he disputed, given that the puck was chest high when he grabbed it.

“I didn’t technically cover it,” de Haan said. “It’s the referee’s call. It was definitely the turning point of the night. Greisser’s been our MVP this series and he was great again.”

After getting to a second overtime, the Islanders started to turn the tide. Jaromir Jagr went off for tripping John Tavares at 5:06, but the Islanders could not convert on the power play.

One overtime power play is a gift; two is a blessing. Derek MacKenzie slashed Tavares’ stick in half with 5:29 left in the second OT, and the Islanders felt they needed to convert.

“You get that second one and you’re thinking, are they going to get one next?” Jack Capuano said. “You have to take advantage.”

And it was Quine, who made his NHL debut two weeks ago after 195 AHL games, winning it as part of a truly makeshift second power-play unit.

Marek Zidlicky, making his series debut, faked a shot and sent it to Quine along the right boards, and he whizzed a shot past Luongo for the unbelievable winner.

“I was just happy to see it go in,” Quine said. “I just wanted to hit it on net. I didn’t see it go in, but I saw everybody celebrate.”

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Now the Islanders return home for tomorrow’s Game 6 with a chance to advance. The way Game 5 went, that seemed almost as unlikely as Quine getting the winner.

“It’s going to be all about our fans and the atmosphere in our building,” Capuano said. “We have to be able to feed off the crowd and come out with some energy.”