PHILADELPHIA — The Islanders felt deflated during the third period against the Flyers on Tuesday night.

They were trailing by a goal after Claude Giroux split two defenders before finishing, and were staring a gut-punch loss in the face. But then, after a hit from Philadelphia’s Zack MacEwen on Scott Mayfield took the Islanders defenseman’s helmet off, Zdeno Chara stepped in.

Chara decisively beat MacEwen in the ensuing fight, and that moment galvanized the Islanders.

“Our bench perked up after that,” head coach Barry Trotz said, “and then our Identity Line came through.”

Casey Cizikas tied the score with his second goal in as many nights off a feed from Mayfield, and Oliver Wahlstrom won it in the ninth round of a marathon shootout, lifting the Islanders to a 4-3 victory that got them back to .500 after more than two months with a losing record.

They first fell below .500 on Nov. 16. The long road back — after the bottom fell out on this season — is the first of many steps they must take in order to achieve their goal of returning to the playoffs for a fourth straight season.

“The confidence comes with playing well, finding ways to win, what have you,” Trotz said. “It’s starting to grow. There’s trust starting to grow, which is key.”

The Islanders have earned points in seven of their past eight games, and will now play seven straight games at home before the All-Star break. They couldn’t ask for a better chance to get back into the postseason race.

“Getting rhythm for us will be real key,” Trotz said. “Obviously we gotta make up some games, they’re gonna be compressed. It’s a challenge. I think this group’s up for the challenge.”

On Tuesday, though, the focus was just to check off the first goal on the list: getting back to .500.

It looked as if the Islanders would fail to do so after Giroux’s goal 4:05 into the third period gave the Flyers a 3-2 lead. But with 4:28 to go, Cizikas scored just his second goal of the season (also his second in two nights) off a Mayfield pass.

In overtime, the Islanders got a huge save by Semyon Varlamov (who finished with 31) on a two-on-one rush. That sent the game to what became the longest shootout in the NHL this season.

Just over two minutes into the game, Robin Salo opened the scoring with a slap shot that got by Carter Hart. But the Flyers found their footing soon after, with James van Riemsdyk scoring at 14:39 on a power play after Cam York’s shot went off the end boards and Varlamov looked to be caught unaware by van Riemsdyk in the crease.

The Islanders took the lead back at 13:28 in the second, when Josh Bailey converted Anthony Beauvillier’s pass to the crease. But they handed it right back less than 30 seconds later, with Travis Konecny scoring after Oskar Lindblom nicked the puck off Varlamov, who was playing it out of his crease.

The Flyers doubled the Islanders’ shot total in the second period, putting them on their heels in the middle of the game for the second night in a row. And for the second night in a row, the Islanders found a way to come away with two points.

It took a Herculean effort from Varlamov. After he stopped nine shots in the shootout, he said: “Today was stressful.”

That it was. And make no mistake: .500 is a paltry milestone to be celebrating in mid-January. But it’s a milestone nonetheless, and the Islanders haven’t had much to be happy with in the last two months.

“That’s a starting point,” Trotz said. “We’re back, [you can say] we got our nose just at the water level. Now see if we can keep climbing up the ladder here.”