The Rangers can breathe a little easier in their quest for the President’s Trophy.

And the Islanders’ path to the playoffs appears inevitable.

After the Islanders handed them defeat earlier this week, the Rangers took revenge on home ice Saturday afternoon, denying the Isles a chance to clinch a postseason berth with a 3-2 overtime victory to move three points clear of the Hurricanes in the Metropolitan Division and set a new franchise record for regular-season wins, with 54, thanks to Vincent Trocheck’s game-winner.

But because the Islanders took home a loser point that extends their playoff cushion to four points with two games remaining in their season, this game felt just as much like a win for the visitors, even as their six-game winning streak was broken.

This one would require the sort of third period in which the Rangers have specialized this season, gathering themselves and coming back after coughing up the lead in the second.

For much of the afternoon, the Rangers appeared a step behind at even strength, struggling to stay in the offensive zone for long periods or gain traction against a bottom six that turned in a superb afternoon.

The Isles had a golden chance to grow their lead to two goals with 6:56 to go after Artemi Panarin took down Adam Pelech on a breakaway to give the defenseman a penalty shot.

But Igor Shesterkin’s glove save ensured the game would stay at 2-1 — an exclamation point on an afternoon in which Shesterkin and Ilya Sorokin both delivered classic performances.

But just over 2:30 later, Panarin beat the other Russian netminder, loosing a wrist shot from the top of the left circle after a faceoff to equalize the game at two.

And following a high-tension five minutes in which both teams traded chances, culminating in Shesterkin’s glove save on Mat Barzal with just seven seconds to go, on it went to the skills competition.

That was where Shersterkin got the last laugh, punctuating his 33 saves with a few more.

Just like the match on Long Island on Tuesday, the Islanders had a five-on-five edge early, but bled chances on special teams.

The difference was that instead of doing so on the penalty kill, they did so Saturday on their own power play.

Thanks to consecutive Rangers penalties including a double minor, the second period opened with 5:07 straight at five-on-four for the visitors.

Not only did the Islanders record just two shots and no high-danger chances while missing Noah Dobson (upper body), but they allowed a shorthanded goal after Braden Schneider followed up his own rebound by potting one 4:33 into the period.

Once the game returned to five-on-five, the Islanders could start gaining traction.

Brock Nelson, who had accounted for just one goal since March 11, broke out of his scoring slump in emphatic fashion, swatting Kyle Palmieri’s rebound in following an acrobatic Shesterkin save to tie it.

Before the period was over, Nelson had given the Islanders the lead, finishing off Hudson Fasching’s wraparound pass to the left circle.

But the Islanders’ season-long habit of playing with their food then going hungry came back to bite them, and their chance at the playoffs will now come down to the final two games of the regular season.

Since the Isles came into the day with a three-point lead for third place in the Metropolitan Division, they could not be knocked out of the spot no matter what happened later in the night.

This loss, however, represented the club’s margin for error in a playoff race that has featured every twist and turn imaginable thus far.

Now, with Dobson’s status in question for the end of the regular season and a six-game winning streak broken, it’s the Islanders who need to stave off chaos if they are to finish the job.

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