It’s right in front of the Islanders now: a chance to win a playoff series — and a chance to do it in front of their own diehard fans, who have endured 22 straight seasons of first-round exits or no playoffs at all.

The key, however, is to not treat Sunday night’s Game 6 against the Panthers at Barclays Center as the most important game just about all of these Islanders have ever played.

“The series isn’t over, far from it, and we have to treat this like it’s an important game, but only because it’s the next one,” John Tavares told Newsday on Saturday just after the team returned from Florida. “We know from experience on both sides of it that the fourth one is the hardest one to get. We know we have a great opportunity at home, in front of our fans, and we want to take advantage of that.”

The Islanders have this opportunity thanks to a wild Game 5 win in double overtime early Saturday morning. It featured superb play by goaltender Thomas Greiss and a clutch game-winner from rookie Alan Quine, who seemed more likely to be readying for the start of the AHL playoffs with Bridgeport than one-timing a shot past Roberto Luongo at 16:00 of the second OT for a 2-1 win that gave the Islanders a 3-2 series lead and pushed them to the brink of advancing.

Quine played on Tavares’ left side Friday night, one of three line shuffles by Jack Capuano to try to balance a top-heavy attack from the first four games.

“You can see the talent he has — he’s tenacious, he’s got good hockey sense and he’s able to create opportunities,” Tavares said. “When you have someone like him come up and be such a big surprise for us, it’s huge.”

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Huge, too, were the two second-overtime power plays the Islanders got. Jaromir Jagr tripped Tavares on a rush at 5:06 of the second OT and the Islanders didn’t convert; Derek MacKenzie slashed Tavares’ stick in half at 15:20 and Quine, part of a real ragtag second power-play unit, converted.

That left the Islanders 5-for-18 (27.8 percent) on the power play in the series, with both OT wins turning on Islanders power-play goals.

“Those guys don’t always get the prime opportunities on the power play, but they still took advantage,” Tavares said. “I thought the first unit with me didn’t have our best night, but we’re clicking with it so far.”

The calls themselves were legitimate, though that isn’t always enough of a justification for one OT power play, let alone two. Perhaps the penalty-shot call in the first overtime, in which referee Ian Walsh ruled that Calvin de Haan covered the puck in the crease, was justification enough.

Greiss denied Aleksander Barkov on the penalty shot and the Islanders played on.

“I thought both refs had a good pulse for that game,” Tavares said. “We’re trying to create opportunities on both plays and that’s when you want the calls to be made, when they do something outside the rules to try and stop you.”

Tavares, who was held off the scoresheet in Game 5 for the first time in the series, knows what awaits Sunday night.

The first two playoff games at Barclays last week were a revelation to every player on the Islanders. Seeing a sellout crowd waving orange towels and turning the team’s new home into a bit of a sound-alike of its old home was a special experience.

“The first two games blew us all out of the water,” Tavares said. “The Coliseum was something special, but in our new home, our fans had a real sense of pride and brought that over from last year.

“Our fans know the opportunity we have [Sunday night], and our goal as players is not to get too carried away but also feed off their energy. It’s the next game and we know how desperate Florida will be, so we have to be able to match that.”