ANAHEIM, Calif. — As the shootout wore on and on, it became almost comical. But there was nothing funny about the Islanders’ desperate need for two points Tuesday and, somehow, they escaped here with both points they had to have.

Nick Leddy ended a 14-round shootout by beating Jonathan Bernier and it will go down as a 3-2 Islanders win that featured yet another third-period lead blown and a calamitous overtime in which Thomas Greiss made seven of his 39 saves on the night.

But the shootout was the epic turning point. The Islanders, shooting last, prolonged it four times, including a review-confirmed goal in the 12th round by Thomas Hickey that left Ducks general manager Bob Murray screaming epithets down the hallway outside the officials room.

“We needed them so bad,” Hickey said after the Isles won their first shootout of the season in three tries. “We need the two tomorrow and the two after that, as well. But it starts here.”

Hickey, the first defenseman up after Jack Capuano used all 11 forwards he had available with Cal Clutterbuck (upper body) sidelined after a big hit in the second period, made a backhand move and appeared to push Bernier’s pad and the puck over the goal line.

The referees ruled it a goal, then reviewed it and determined there was no goaltender interference — a decision that left Ducks coach Randy Carlyle apoplectic and a few Islanders raising their eyebrows at their good fortune.

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That luck has been in short supply this season but the Islanders earned some Tuesday, rallying from a quick 1-0 hole after Cam Fowler’s power-play shot ticked off Clutterbuck’s skate and past Greiss just 1:04 in.

“We were pretty resilient from that point on,” Andrew Ladd said. “It’s good to see us respond like that.”

Adam Pelech tied the game with his first career goal at 11:51 of the first and Josh Bailey, who had a strong night, put the Isles in front with a one-timer on the power play at 16:42.

Greiss preserved the one-goal lead until Rickard Rakell beat him with 10:52 left in the third. A wild final few minutes of regulation featured an Islanders power play, their fifth of the night, and an open net for Brock Nelson off a rebound that he could not corral. Soon after Ryan Kesler rang a shot off the crossbar and Greiss got a piece of Ryan Getzlaf’s ripper to get the Isles at least a point.

It was all Greiss in an ugly overtime.

“Yeah, we might need to work on that three-one-three a bit more,” Ladd said. “Greisser was huge.”

Hickey said:“He’s so calm out there, it really spills over to everyone. Even in the shootout, he’s just an old-school, stand-up style goaltender who doesn’t let much get to him.”

John Tavares (round four), Ryan Strome (round six), Nikolay Kulemin (round eight) and Hickey kept the shootout going until Leddy won it. The Islanders are still in last in the Eastern Conference but able to breathe easy for the first time in a few weeks.

“They deserve to get some bounces going our way,” Capuano said. “We’ve battled through enough adversity that we didn’t let anything get to us tonight.”