They didn’t exactly fix their problems Monday night, but enough went right for the Islanders to get a win and two points they had to have.

Thomas Hickey’s deflection of John Tavares’ backhand flip squeezed past Flames goaltender Brian Elliott at 1:53 of overtime for a 2-1 Islanders win at Barclays Center, their first non-shootout victory since Nov. 7. They had gone 1-4-2 in that span.

They still had trouble scoring goals, posting fewer than three for the eighth straight game.

They still had trouble holding a third-period lead, letting a 1-0 edge slip 5:51 into the third period and allowing the struggling Flames to hang around and take charge of the game for stretches of the final two periods.

But there’s not much time for self-reflection when you’re at the bottom of the standings.

“It’s a team that’s in the West, so we have to worry more about getting the two points than giving up one,” said Hickey, who scored his fifth overtime winner (four regular season, one playoffs) of his 16 career goals.

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The Islanders got a break in overtime when the Flames’ Michael Frolik broke his stick while the Isles had possession.

Frolik went to the bench to change, as did Casey Cizikas, who allowed Tavares to hop over the boards and pick up a pass from Shane Prince.

With a Flames forward racing to get back in the play, Tavares drew both remaining Flames to him and flipped a backhander toward the net, where Hickey tipped it out of midair and behind Elliott for the winner.

“They had that broken stick — we’ve been looking for a bounce lately and complaining we haven’t gotten any,” Hickey said. “We got one there and it worked out pretty well.”

The Islanders had four power plays to Calgary’s one, including a gift advantage with 4:51 to play in the third. That’s been the dangerous time for the Islanders to lose points in tied games, as they did on the last two stops of their California trip last week.

But with a chance to grab the lead back, the Islanders’ power play fizzled against the Flames’ 29th-ranked penalty kill. The Isles had no shots on goal and played the remainder of regulation quietly.

“Even if you don’t score there, a good power play gives you a little bit of a surge that you need,” Islanders coach Jack Capuano said. “We couldn’t get anything going.”

The Islanders did start this game well, playing a strong first period in which they allowed only 13 shots, four of them on Thomas Greiss. Tavares picked up a neat drop pass from Josh Bailey and snapped one past Elliott at 7:32 for the captain’s first goal in 10 games.

“About time,” said Tavares, who had his first multi-point game in the last 15. “We’d love to come away with more than one. We’ve got to find a way to keep pushing, keep generating chances.”

Thomas Hickey, left, celebrates his game-winning goal in overtime as the Islanders beat the Flames, 2-1, in overtime at the Barclays Center on November 28, 2016. Photo Credit: Getty Images / Bruce Bennett

Even with two second-period power plays, the Islanders faded, with Greiss (25 saves) stepping to the fore with some strong play.

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He had no chance on Sean Monahan’s tying goal but again was sharp, helping keep it tied through the bulk of the third period.

There’s still loads of work to do, but the Islanders head into the Penguins/Capitals gantlet tomorrow at home and Thursday in Washington feeling a bit better.

“I don’t think anyone’s going to complain about the win,” Tavares said. “We’ve still got some things we need to work on.”