After a week of falling behind and usually failing to catch up, the Islanders needed to come out charging on Tuesday night against the 30th-place Blue Jackets.

It wasn’t a perfect first period, but it was good. And the Islanders kept pushing the pace, led by Brock Nelson’s first NHL hat trick in a 5-2 win over John Tortorella’s Columbus squad at Barclays Center.

Coming off a Saturday washout in Philadelphia when the Islanders managed just two first-period shots, there was plenty of incentive to start strong and the 17 first-period shots on Tuesday told a different story.

“That was atrocious,” Brian Strait said of the 4-0 loss to the Flyers. “Everybody brought it tonight.”

Right off the opening draw, Nikolay Kulemin nearly shoveled a loose puck under rookie Blue Jackets goaltender Anton Forsberg, who was making his ninth NHL appearance.

Ryan Strome found a gift in the crease 5:03 in, sweeping home his first in 17 games after Forsberg dropped Matt Martin’s soft toss from the point. Jack Capuano scrambled two of his first three lines, moving Mikhail Grabovski to the wing with John Tavares and Strome while putting Nelson in the middle for the first time all year between Anders Lee and Josh Bailey.

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There were results for all. “It felt good to contribute,” Strome said. “I could have had 2-3 more and that’s a little frustrating. But we had a lot going in the first and third, we were creating a lot.”

The shots were 11-0 when Columbus got its first crack at Thomas Greiss, and it was 1-1 on the board at 10:26 when William Karlsson smacked in a rebound on the Jackets’ second shot.

But Nelson answered 1:34 later, snapping a wrist shot from his off wing past Forsberg. The visitors played a more vibrant second and evened the score on David Savard’s hard knuckler from the point at 13:49, but there was Nelson again at 17:29, chipping one past Savard to start a two on one that he finished with a quick shot between Forsberg’s legs to restore the Isles lead heading to the third.

“We had all the momentum after the first goal so you can’t get too down when they push back,” Nelson said. “You control the play for as long as we did, you’re going to get a break.”

They got one to extend the lead at 5:34 of the third. Tavares (along with Nelson) set up Strait at the point and his untouched slapper got through Forsberg, a rare goal for Strait. “That’s what Cappy always says,” Strait said, chanting a Jack Capuano mantra. “Shoot the puck, good things happen. They did for me tonight.”

Nelson wrestled one into an empty net with 10.8 seconds to play to bring the hats down to the Barclays Center ice and secure the Isles win, a much-needed turnaround after three straight divisional losses by a 13-3 combined score. The Rangers come to Brooklyn on Thursday with both teams sitting at 51 points, a huge game for confidence between two teams that have been treading water for a month.

“It was a good bounce-back off Saturday,” said Nelson, now the team leader with 17 goals. “We got back to some of the things that made us successful last year, getting on teams early and working in their zone.”