Arizona Coyotes defenseman Troy Stecher loses the puck to New...

Arizona Coyotes defenseman Troy Stecher loses the puck to New York Rangers center Ryan Carpenter during the third period on Nov. 13, 2022. Credit: AP/John Munson

The Rangers were going nowhere fast Sunday in their game against the Arizona Coyotes. They were 1-3-1 in their last five games; they were playing their third game in four nights — a one-shot home game before leaving for a four-game West Coast trip Tuesday — and their legs were dead.

And then, they started taking penalties. Which, it turns out, is what saved them.

“They were winning all the loose-puck battles, and they were first on pucks,’’ Rangers coach Gerard Gallant said after what ended up being a 4-1 Rangers victory. “It was a tough travel [experience], and three in four nights for us. And you don't make excuses, but that has something to do with it. And I just thought we were slow, and then all of a sudden . . . those two PKs were good for us, to get our legs going.’’

The Coyotes had outshot the Rangers 17-4 in the first period, but Igor Shesterkin (31 saves in the game) was solid and kept it scoreless before Ryan Carpenter was sent off for an interference penalty at 9:49 of the second period, giving Arizona its third power play.

The Coyotes entered Sunday with the league’s third-best power play, having scored 15 goals in 48 attempts (31.25%) in their first 14 games. But the Rangers’ penalty kill shut them down on their first five attempts, and Chris Kreider, one of the Rangers’ key penalty-killing forwards, said the Carpenter penalty was the turning point in the game.

“I thought we were starting to get to the net, starting to get inside, [and I] didn't necessarily agree with that call,’’ Kreider said. “I thought the penalty kill did a good job. And we started generating some chances shorthanded, and then that carried over into 5-on-5.’’

Little more than a minute after Carpenter’s penalty expired, Vincent Trocheck was called for an interference penalty, and the Rangers killed that one, too. Then, 16 seconds after Trocheck exited the penalty box, the Rangers got some pressure on the Coyotes in their zone, and Barclay Goodrow cashed in off a turnover and scored at 15:05 to give the Rangers the lead. Adam Fox’s goal, 1:18 later, put them up 2-0, and the Rangers never looked back.

“Obviously, you want to score on the power play and keep the puck out of your net on the kill,’’ Kreider said. “But to be able to tilt the ice, whether it's generating chances on the power play, or denying them the zone on the kill, yeah, that's definitely something that you can take little energy from.’’

The Rangers’ penalty kill began Monday as the 11th best in the NHL, with a success rate of 81.5% (10 goals allowed in 54 times shorthanded), and they have scored two shorthanded goals. They killed five of six Sunday, finally allowing Clayton Keller’s goal at 8:33 of the third period when the Rangers were up 3-0, but when the Rangers needed a spark, the penalty kill gave it to them.

“We had a couple [shorthanded] opportunities, jumped on that and we got chances going the other way, and those were the best chances,’’ Gallant said. “And that's really why I think our team changed from that point on. I really do.’’

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