Rangers beat Hurricanes 5-2 at the Garden to force a Game 7

The Rangers didn’t run the Carolina Hurricanes out of the Garden on Saturday night as much as Igor Shesterkin wouldn’t let them in.

Early goals by Tyler Motte and Mika Zibanejad lit the flame for a 5-2 Game 6 win, the Blueshirts’ sixth straight at home, to force a do-or-die Game 7 Monday night in Raleigh, N.C.

“Again, our backs were against the wall tonight, and we played our best hockey,” head coach Gerard Gallant said.

Flashy young center Filip Chytil scored twice in the second period to create important breathing room, prompting Carolina coach Rod Brind’Amour to pull shaky goalie Antti Raanta down 3-0 just 3:24 into the second frame.

But Carolina was fully prepared to end the Rangers’ season anyway, even after facing a 2-0 deficit 9:51 into the first period on Zibanejad’s slick power-play goal.

And Shesterkin just wouldn’t allow a Hurricanes comeback, while flashing the competitive fire that Gallant’s team will need to earn its first win on Carolina’s ice and advance.

The Vezina Trophy finalist was brilliant at handling an early Canes onslaught, making nine saves in a span of two minutes and 19 seconds between the 13:28 and 15:47 marks of the first.

He flashed his glove throughout the match to rob Tony DeAngelo, Jordan Martinook and Vincent Trocheck. He registered two assists of his own on Ranger goals.

And he got in the Hurricanes’ faces late in the second period while up 4-2, burying Seth Jarvis near the crease after making a left pad stop on the Carolina winger.

“It’s always great to have a goalie whose next step is only to just start scoring goals,” winger Artemi Panarin cracked of Shesterkin’s all-encompassing impact.

Shesterkin was assessed a minor penalty for interference after smashing his glove into Jarvis’ face and knocking him to the ice. But it was well worth it to see the team’s on-ice leader become its emotional engine, too.

“To be honest, [Jarvis] was a bit on the smaller side,” Shesterkin said through a translator, with a wry smile. “If he was a bit bigger, I probably would have been the one who fell.”

He then barked at Carolina forwards Sebastian Aho and Max Domi as they griped, and nodded his head up and down in a cocky strut, as if he were telling Aho to do something about it.

The Hurricanes plan to do something about it Monday at home, where they are an undefeated 7-0 in this postseason compared to a putrid 0-6 record on the road.

The Rangers will count on their 4-0 record in closeout games so far through two series, including their comeback from 3-1 down against the Pittsburgh Penguins in the first round.

“We’ve had our backs against the wall in these playoffs, and I think we know how to play when we’re in this situation,” defenseman Adam Fox said.

Gallant’s Blueshirts have won one road game in six tries this postseason: a 5-3 victory at Pittsburgh in Game 6 of the first round. Zibanejad and Chris Kreider each scored twice in that victory, and Shesterkin made 31 saves.

It wasn’t all the goalie Thursday night against the Hurricanes, either. Shesterkin had been excellent in Game 5 at Carolina, only to see his Rangers offense meekly snuffed out, 3-1.

On Saturday, though, the Rangers scored early and then padded their lead once Carolina broke through.

Chytil, 22, scored twice after notching zero points in his last four, not coincidentally while reunited on “The Kid Line” with wingers Alexis Lafreniere and Kaapo Kakko.

Chytil’s second goal was scored on the Rangers’ first shot aimed at backup goalie Pyotr Kochetkov when he replaced Raanta. The Czech center snapped a terrific backhand shot from the left circle over a stunned Kochetkov’s right shoulder.

The Hurricanes’ shaky goaltending could lead Brind’Amour to turn to Frederick Andersen for Game 7, if Carolina’s regular season No. 1 is deemed healthy, having missed all of the playoffs to date with a lower body injury.

As it was, plenty of Rangers got in on Saturday’s action.

Fox posted two assists, giving at least one point in four straight. Zibanejad now has goals in four straight games and a team-leading seven in this postseason.

Regular season points leader Panarin added an important third period insurance goal on the power play, his first goal since his Game 7 overtime winner against the Penguins.

Fourth-line center Barclay Goodrow even made a surprise return to the lineup, despite reportedly breaking his ankle in Game 1 of the first round against Pittsburgh.

Shesterkin set the table for everything, though, right from the start.

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With the game scoreless, he stopped Aho and Teuvo Teravainen in close, before Motte charged up ice and scored on a 40-foot wrist shot that Raanta should have had 7:22 in.

Zibanejad kept Raanta off kilter by lifting his left skate and faking a move to the right side of the net before suddenly sliding the puck five-hole on the frozen goaltender.

The Hurricanes didn’t waver, though. They actually put 15 shots on goal in the first period alone, nearly matching the Rangers’ total of 17 for all of Game 5 in Raleigh. And they still came up empty, trailing 2-0 after one.

Hurricanes defenseman Brady Skjei broke through on a wrist shot 5:05 into the second period to draw within 3-1, with Shesterkin screened by two of his own men.

And Trocheck narrowed the Blueshirts’ lead to 4-2 at 12:47 of the second period on a rebound after a brilliant Shesterkin save on a deflection in front.

But Chytil and Panarin answered both goals with Ranger tallies that kept the Garden rocking. Now they have to finish the job away from home.

“We have to play how we play at home,” Chytil said. “Last series, we found a way to win in Pittsburgh. It’s Game 7 now and we have to find a way. Play hard, play our game, don’t focus on anything else, and I think we can win the game.”