Rangers goaltender Igor Shesterkin makes a save against the Hurricanes...

Rangers goaltender Igor Shesterkin makes a save against the Hurricanes during the second period of Game 3 of an NHL Stanley Cup second-round playoff series Sunday at Madison Square Garden. Credit: AP/Adam Hunger

After two tight defensive efforts — and two losses — in the first two games of their second-round playoff series against the Carolina Hurricanes, the Rangers knew they had to change things up Sunday in Game 3. And whether it was by design or not, things loosened up a bit as the series shifted to Madison Square Garden.

That allowed the Rangers to create a few more scoring chances. And even though it meant also allowing a few more scoring chances for their opponent, that was OK, because goaltender Igor Shesterkin was at the top of his game, there to save the Rangers when they needed him to do so.

Shesterkin, the likely Vezina Trophy winner as the NHL’s best goalie in the regular season, turned in a vintage 43-save performance and the Rangers finally got some goals, enough to beat the Hurricanes, 3-1, and cut their deficit in the best-of-seven series to 2-1.

“We killed some penalties, scored a power-play goal. That’s how you win hockey games, and tight games,’’ coach Gerard Gallant said. “It was a tight battle again tonight. Obviously, Igor was outstanding for us, and that was the key.’’

Mika Zibanejad’s first-period power-play goal — the Rangers’ first man-advantage goal of the series — and Chris Kreider’s second-period goal, his sixth of the playoffs, provided all the offense the Rangers needed.

Tyler Motte’s first goal as a Ranger, into an empty net with 1:23 remaining, sealed the result. He backhanded a soft shot from just behind his own blue line moments after Kreider missed the empty net from inside the offensive zone.

Gallant shook things up from the beginning, breaking up his “Kid Line’’ of Alexis Lafreniere, Filip Chytil and Kaapo Kakko and placing each youngster with a different top-three line.

Chytil, who has played mostly center all season, was assigned to the right wing of the first line, with Kreider and Zibanejad, and that line generated a lot of chances throughout the game.

“It’s a coach’s decision,’’ Chytil said of him playing the wing. “I didn’t mind it. Kreids and Mika are top players on our team, and that was just good just to play with them.

“I had a lot of great chances. As a line, we had a lot of good chances. We scored a goal, we had a penalty against, and then we scored a goal in power play. So I think the first two periods were great. We were playing in the right way, and that was a good experience for me.’’

Lafreniere played right wing on the second line, with Artemi Panarin and Ryan Strome. Kakko stayed on the third line with two new linemates, Frank Vatrano on the left and Andrew Copp in the middle.

The lines stayed together for most of the first two periods. However, with the Rangers holding a 2-1 lead late in the second period — Nino Niederreiter’s goal at 8:18 of the second period had halved what was a 2-0 Rangers lead — Gallant reunited the Kid Line and went back to the lines he’d used in the first two games of the series and for most of the playoffs.

“I just wanted to get Copper in the middle, you know, a stronger faceoff guy in the dot,’’ Gallant said. “And you know, he did pretty well [winning 10 of 16], but we still had a lot of trouble at the faceoff dot [the Rangers won only 27 of 63] tonight. But that was the thinking early on.’’

Zibanejad got the party started, first drawing a penalty when he was held by former teammate Brady Skjei, then blasting home a one-timer from the left circle off a pass from Panarin at 11:54 of the first period to make it 1-0.

Kreider made it 2-0 when he walked out from behind the net and lifted a wrist shot over the right shoulder of Carolina goalie Antti Raanta at 5:55 of the second period. Former Ranger Tony DeAngelo, the target of boos by the Garden crowd all night, had lost his stick on the play, and Kreider took advantage.

Niederreiter’s goal made it 2-1, but Shesterkin shut the door after that.

“I think we sat back a little bit too much when we got the lead,’’ Kreider said. “But all three games have been really, really close games, could have gone either way. And you know, that’s playoff hockey, so you’ve just got to continue to work for your bounces.’’

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