RALEIGH, N.C. — There was no time for a tired Tuesday night, no room to let fatigue prevail.

No, even though the Islanders have bounced from state to state and country to country and were playing a back-to-back, this team could absolutely not afford to give up. Not even when the Hurricanes took a two-goal lead, and not when the game spilled over into overtime.

And so, they did what any weary traveler does. They blasted the proverbial music, pumped up as much energy as they could muster, and resolutely refused to fall asleep at the wheel.

John Tavares scored on a feed from Joshua Ho-Sang — who picked up a turnover in the neutral zone — 34 seconds into overtime, as the Islanders rallied to beat the Hurricanes, 3-2 at PNC Arena. With the Maple Leafs losing, the Islanders are now tied with the Lightning at 77 points for the final wild card spot in the Eastern Conference.

“It’s huge,” Doug Weight said. “It’s huge for the standings, but it’s also huge for our psyche. We got through a really, really long road trip. The circumstance hasn’t been great for our travel and everything else and we’ve got to get home now to our bed and we’ve got a couple home games. So it’s exciting for us, that’s for sure.”

The Islanders returned home from a nine-game road trip and on Monday promptly gave up eight goals to this Hurricanes team before boarding a plane and beating the storm out of New York. And, for the opening period of Tuesday’s game, they wore their brutal schedule plainly. They struggled to maintain any offensive momentum as the Hurricanes broke the ice 12:30 into the game.

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Thomas Hickey turned the puck over to Lucas Wallmark near the boards, and Wallmark fed Joakim Nordstrom in the right circle. Nordstrom’s snap shot bounced past Thomas Greiss on the blocker side. Elias Lindholm made it a two-goal game in the opening minute of the second period, with a quick release on a breakaway that beat Greiss. The game had disaster all over it after that, until Greiss truly took over and Ho-Sang converted.

At 18:55, Ho-Sang took advantage of the Hurricanes’ slumbering defense near the net, on a wrister to Cam Ward’s short side. With 40 seconds left in the period, Jason Chimera’s shot hit the crossbar and bounced in for the tie.

“It’s a big character win,” Tavares said. “It was a good job by everyone kind of staying with it instead of being discouraged and being frustrated. The game started to turn for us in the second half of that (second period) and we started generating more opportunities and limiting that time and space.”

Greiss was brilliant down the stretch — pivotal in quashing the Hurricanes’ three power-play opportunities. With 17 minutes left in the game, Brett Pesce passed it deep to Jeff Skinner on a breakaway. Skinner, who beat Greiss on a penalty shot on Monday, wasn’t quite so successful Tuesday. With defenseman Dennis Seidenberg trailing behind him, Skinner tried to get by Greiss’ glove side, but was denied.

“He kept us in the game,” Weight said. “It works like that. Guys are behind them. They really like our goaltenders and we came back and tied the game at the end of the period.”

Ho-Sang now has a three-game point streak — amassing two goals and three assists in that stretch. Weight said that though he had high hopes from him, even he is a bit taken aback by his progress.

“Watching him play, I was like ‘Geez, he’s going to have a good career, but he’s got to learn a lot of things,’” Weight said. “So, yeah, I am (surprised). I don’t think I’m astonished, but I’m pleasantly surprised at how fast he’s come along . . . I had him out there with three minutes left in a 2-2 game that’s arguably our biggest of the year, so that’s a pretty good sign.”

And now, they get to celebrate the best way they can: A day off.