New York Rangers left wing Artemi Panarin (c.) celebrates his...

New York Rangers left wing Artemi Panarin (c.) celebrates his goal with Adam Fox (23) and Vincent Trocheck (16) in the third period against the New York Islanders at Madison Square Garden, Saturday, April 13, 2024, in New York. Credit: Corey Sipkin

Before the start of overtime Saturday afternoon, Islanders forward Mathew Barzal teased Rangers goalie Igor Shesterkin about what to expect in the five-minute extra period.

“He told me before the overtime started, he said, ‘Shesty, waiting for high glove,’  ’’ Shesterkin said. “I said, ‘OK.’  ’’

So with less than 10 seconds remaining in overtime, here came Barzal, flying into the Rangers’ zone, with a chance to win the game. The shot went high to the glove side, just as Barzal had promised. Shesterkin windmilled his glove arm upward and grabbed it, making the last of his 33 saves in regulation and overtime and sending the game to a shootout.

Shesterkin then stopped both of the Islanders’ shootout attempts and Artemi Panarin and Vincent Trocheck scored against Ilya Sorokin to give the Rangers a thrilling 3-2 comeback victory in a game that had plenty of playoff implications — and the potential of being a preview of a first-round series.

“It was a good game,’’ said Sorokin, who made 41 saves in regulation and overtime. “It’s sad they get the two points.”

The Rangers are 54-23-4 and set a franchise record for wins in a season. They already had tied the 2014-15 team with 53.

“The fact that this group was able to battle hard the way they did and collect 54 [wins], I think that’s something they should be proud of from a regular-season standpoint,’’ Rangers coach Peter Laviolette said. “But . . . there’s a lot of work that has to be done.”

The victory gave the Rangers 112 points and a three-point lead over second-place Carolina in the Metropolitan Division. It also gave them the tiebreaker (most wins) over the Hurricanes. Carolina is 51-22-7 with two games remaining on Sunday at Chicago and on Tuesday at Columbus. To win the division title, the Hurricanes need to win both games and have the Rangers lose in regulation to Ottawa.

With the one point earned from the game, the Islanders (37-27-16, 90 points) put themselves on the brink of qualifying for the playoffs. They needed both Washington and Detroit to lose in regulation on Saturday night, but both teams won.

Panarin scored the third-period goal that forced overtime. The Islanders led 2-1 entering the third on the strength of two second-period goals by Brock Nelson. They also had chances to score insurance goals in the third, most notably when defenseman Adam Pelech was awarded a penalty shot with 6:56 remaining in regulation.

But Shesterkin came up big. He went post to post and did the splits to stop a shot by Hudson Fasching at 6:45 of the third, then got his pads on Pelech’s penalty shot to keep the Rangers within 2-1.

“We had really good chances in the third to make it a 3-1 game,’’ Islanders coach Patrick Roy said. “Penalty shot, [Jean-Gabriel] Pageau had an open net, [Casey] Cizikas hit the crossbar. I was pretty proud of the way our guys were responding to the push they made at the start of the third period.’’

But when the Islanders left the door open, Panarin walked through it. Trocheck won a faceoff in the left circle back to Panarin, who rocketed a shot from the top of the circle over Sorokin’s glove to tie it with 4:17 left.

“I tried to find the [shooting] lanes. I didn’t really see the goalie,’’ Panarin said of his 48th goal. “I tried to just put the puck between the legs. I think it touched someone, a defenseman.’’

After a scoreless first period, the Rangers got the game’s first goal, a shorthanded effort by defenseman Braden Schneider at 4:33 of the second period. Pierre Engvall appeared to tie it for the Islanders 38 seconds later, but his one-timer was taken off the board after the Rangers challenged the play and video review found the Islanders to have entered the zone offside.

Nelson tied it at 11:42 of the period, banging in his own rebound off Shesterkin for his 31st goal. His second goal came with 27.2 seconds left in the second period and put the Islanders in front.

Kyle Palmieri and Fasching won a two-on-two battle for the puck behind the net against Rangers defensemen K’Andre Miller and Schneider, and Fasching came around the right wing goalpost and sent a backhand pass across the crease to Nelson, who banged it in.

CLINCHING SCENARIOS IN PLAY

The Islanders came closer to a playoff berth with Saturday afternoon’s 3-2 shootout loss to the Rangers at Madison Square Garden, but they did not get the help needed to clinch.

The Capitals’ 4-2 win over the visiting Lightning ended the Islanders’ chance of clinching on Saturday. Thanks to the Penguins’ 6-4 loss to the Bruins on Saturday night, the Islanders can clinch third in the division with a win over the Devils on Monday night at Prudential Center. That would give them 92 points; the Capitals cannot get more than 91 and the Penguins cannot get more than 90.

The Rangers now stand a good chance of finishing first in both the Eastern Conference and the Metropolitan Division. They can clinch the conference and division titles with a win over the visiting Senators on Monday night. The same would happen if the second-place Hurricanes lose either of their last two games against Chicago and Columbus. — Andrew Gross