Islanders center Anthony Beauvillier is congratulated by teammates after scoring...

Islanders center Anthony Beauvillier is congratulated by teammates after scoring a goal against Rangers goaltender Ondrej Pavelec during the first period of an NHL hockey game at Madison Square Garden on Saturday, Jan. 13, 2018. Credit: Kathleen Malone-Van Dyke

Entering Saturday’s game at Madison Square Garden, neither the Islanders nor the Rangers had won a game in regulation since before Christmas. One of them played as if they might not do so until Groundhog Day.

Behind big games from Mathew Barzal and Anthony Beauvillier — 20-year-olds born within two weeks of one another in 1997 — the Islanders blew out the Rangers, 7-2, to further tighten the playoff picture in the Eastern Conference.

The Rangers (22-16-5) have 49 points. The Islanders (22-18-4) have 48 points. Should be an interesting winter.

Both teams had been off since last Sunday for their midseason breaks. One looked fresher than the other.

“It’s kind of tough coming off a break like that,” the Islanders’ Cal Clutterbuck said. “You never know how you’re going to feel, how you’re going to react. We just wanted to come out and keep it simple, play hard.”

That they did, racing to a 5-1 lead early in the second period, chasing starting goaltender Ondrej Pavelec and drawing boos from Rangers fans who watched the Islanders win for the 10th time in their last 12 visits to the Garden.

“I was surprised,” said Henrik Lundqvist, who was supposed to have the day off in advance of Sunday’s game in Pittsburgh but had to relieve Pavelec. “Mostly, I’m just disappointed.”

Mostly, the Rangers lamented the many odd-man rushes they yielded. Barzal had two goals and three assists, Beauvillier finished with two goals and one assist and Jordan Eberle had four assists. Barzal and Beauvillier each was a plus-5.

According to the NHL, Barzal joined Bryan Trottier as the only Islanders with two five-point games in their rookie seasons.

“Not being smart — way too many odd-man looks,” Rangers captain Ryan McDonagh said of what went wrong. “That’s kind of a byproduct. I think the main thing is we want a group in there that’s willing to do whatever it takes to win. Right now, we don’t have enough guys doing that.”

Ouch.

The Islanders arrived at the Garden banged up and with a new man, winger Michael Dal Colle in the lineup. Then they lost another key player when Casey Cizikas left with an upper-body injury. Coach Doug Weight gave an ominous early prognosis, saying Cizikas likely will miss some time.

“We’re going to have to find a way,” Weight said of surviving the injury bug.

The way the game began was no surprise, given the Rangers’ recent habit of slow starts.

The visitors took the lead 6:06 into the game on a play that began with Barzal niftily carrying the puck out of his zone. He found Eberle, who passed to Beauvillier, who was lurking alone in the slot. Beauvillier ricocheted the puck in off the post to Pavelec’s right.

Hayes tied it for the Rangers, but Shane Prince got a quick rush up ice and snapped a shot from the right circle over Pavelec for his first goal since Dec. 31, 2016, to give the Islanders a 2-1 lead at the first intermission.

Barzal made it 3-1 only 37 seconds into the second period with a fantastic goal on which he rushed up ice himself, skated across the slot and roofed a backhand over Pavelec’s glove side.

“You can’t really pick those spots; it was just kind of lucky to find its way in,” Barzal said. “I don’t know if I was surprised. I was happy.”

At 4:11, Barzal was at it again, putting the Islanders ahead 4-1. On a give-and-go with Beauvillier, the rookie put in his own rebound, continuing to build his case for the Calder Trophy. Barzal took the league lead in rookie scoring with 44 points, four ahead of the Canucks’ Brock Boeser.

The assault continued at 6:51 as Beauvillier beat Pavelec for his second goal to make it 5-1, prompting coach Alain Vigneault to go to Lundqvist.

The Islanders have won two games in a row after breaking a five-game losing streak with a shootout win over the Devils.

“Just one of those nights where everything finds its way into the back of the net,” Barzal said. “We’re going to see them again [Feb. 15 in Brooklyn] and they’ll come out guns a-blazin’.”

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