GREENBURGH, N.Y. — Here’s a twist: A Rangers coach saying the Blueshirts can learn a thing or two from the rival Islanders.

First lesson: Play with more urgency.

“I don’t believe at all that the New York Islanders are a last-place team, but in the standings at this time they are [in the Eastern Conference],” coach Alain Vigneault said Friday. “But in the last two days, they beat the Stanley Cup champions, and the next day, they had the President’s Trophy-winning team waiting for them fresh, at home, and they beat them. That’s how competitive the NHL is: Any team on any given night can beat any other team. And urgency is part of the equation for playing well . . . Players have to be ready, they’ve got to prepare themselves and play with urgency.”

The Rangers, who are 3-4-1 in their last eight, at times have appeared to lack the requisite urgency. They fell behind 1-0 in five of the eight games, and in one of the two games against the Penguins, scored first and then allowed six straight goals.

Do some Rangers, Vigneault was asked, not fully realize that urgency is a factor in today’s NHL? Or does desperation have to seep in, as in the case of the Islanders?

No, Vigneault said, players “do know that urgency is part of the equation — like preparation, like hard work, like execution — of finding a way of being on the right side of the win column. There’s no doubt.”

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Still, too many Rangers, from Henrik Lundqvist on out, have swayed from sharp to unsteady since Nov. 18. How then to flip the switch?

In the case of defenseman Kevin Klein, a lack of urgency prompted a benching for Thursday’s Sabres game.

“Kevin is a gritty, defensive-type defenseman that plays with some jam, and he can chip in now and then offensively when the opportunity is there,” Vigneault said. “I just felt that in the last little while there wasn’t enough urgency to his game. I’m hoping to see that [Saturday against the Hurricanes], a little bit of bite; he’s been a very reliable player in the past, maybe his game had just slipped a little.”

The Blueshirts play the resurgent Islanders on Tuesday, but the slide could deepen before heading to Brooklyn. For Vigneault, some more urgency, starting in Saturday’s matinee, couldn’t hurt.

Notes & quotes: J.T. Miller is expected to dress against the Hurricanes, although he didn’t practice Friday because of a “nagging” kneecap, which is stitched after being cut by Mats Zuccarello’s shot on Sunday . . . Lundqvist will start against Carolina for the second time in five days. He made 26 saves in Tuesday’s 3-2 win . . . Matt Puempel, who did not play in the third period in Buffalo after his elbow was cut by a shot in the second, said he was fine.