Rangers goaltender Igor Shesterkin, center, looks on from the bench...

Rangers goaltender Igor Shesterkin, center, looks on from the bench after being replaced by Alexandar Georgiev during the third period in Game 4 of an NHL Stanley Cup first-round playoff series against the Penguins in Pittsburgh on Monday. Credit: AP/Gene J. Puskar

PITTSBURGH — The Rangers waited five years and lived through a complete rebuild before returning to the playoffs this spring. Now they are staring at the reality that the experience could be short-lived.

Thanks to a shocking defensive meltdown Monday night, the Rangers were pushed to the brink of playoff elimination by the Pittsburgh Penguins, who pummeled them, 7-2, at PPG Paints Arena and took a 3-1 lead in the best-of-seven first-round playoff series. Pittsburgh can close out the series by winning Game 5 on Wednesday at Madison Square Garden.

“I don’t think you’re going to find a guy who’s happy with that performance,’’ defenseman Jacob Trouba said. “There’s not really a whole lot to say past that. I think we know we’ve got to be better, to a man. And . . . we’re gonna show up to Game 5 and put that behind us, be ready to play.’’

Of 326 previous teams that trailed 3-1 in a best-of-seven series, 30 of them (9.2%) managed to win three straight games to win the series. The last team to do it was last year’s Montreal Canadiens, who rallied from 3-1 down to beat the Toronto Maple Leafs in the first round.

Igor Shesterkin, the presumptive winner of this season’s Vezina Trophy as the NHL’s best goaltender, was pulled from the net for the second straight game after giving up six goals on 30 shots in the first two periods. On Saturday, he was pulled from Game 3 after one period, having allowed four goals on 15 shots.

Gerard Gallant didn’t wait to be asked the question about whether he will start Shesterkin in Game 5. He will, he said.

“Yes,’’ Gallant said. “He’s the best goalie in the league, so I’m going to go with him.’’

Gallant was disgusted with his team’s defensive play. He noted that three of the goals that went in against Shesterkin were deflected, and the coach called his team “soft’’ in its defensive play.

“We were soft all over the ice,’’ he said. “There wasn’t much commitment to playing defense tonight.’’

The Penguins have made the postseason for 16 straight seasons, the longest such streak in North American professional sports. Given that 10 of the 23 Rangers who have played in this series either had not played a playoff game or had seen action only in the 2020 bubble playoffs in Toronto in the three-game qualifying series loss to Carolina, Gallant was asked if he thought the difference in experience between the teams showed.

“I wouldn’t use the word ‘inexperienced,’ ’’ he said. “I’d use the words ‘not committed to play in the right way.’ And I mean, we played the right way in New York; there’s no reason why we can’t play the right way tonight. And it’s not from the inexperienced guys, either. I mean, they’re a part of our group, but tonight, you’ve seen a lot of soft, bad plays by a lot of people.

“It was a team effort tonight.’’

The Rangers took an early lead when Alexis Lafreniere, 20, scored his first playoff goal at 2:06 of the first period. But Sidney Crosby, who had been a thorn in the Rangers’ side all series, tied it with a power-play goal at 11:17 when he jammed in a puck that was underneath Shesterkin’s pad but hadn’t been fully frozen for a play stoppage. The referees on the ice initially didn’t make a call of whether it was a goal, but video replay determined the puck had crossed the goal line, so the goal stood.

Things went south quickly in the second period for the Rangers and Shesterkin. Defenseman Mike Matheson’s shot from the blue line deflected off Rangers forward Frank Vatrano and got by Shesterkin at 3:14. Just 24 seconds later, Jake Guentzel slipped behind Adam Fox and got to the back post to tap in a pass from Bryan Rust to make it 3-1. It was Guentzel’s fifth goal of the series.

Defenseman Mark Friedman’s seeing-eye shot from the blue line got through a screened Shesterkin to make it 4-1 at 11:22 of the period. Fox’s bad-angle shot from the left boards deflected in off Matheson’s skate to pull the Rangers within 4-2 at 14:04, but any thoughts of a momentum shift disappeared when Danton Heinen deflected in a shot from Kris Letang to make it 5-2 at 18:53. Jeff Carter deflected in a shot by Jason Zucker with 32.0 seconds left in the period to make it 6-2.

Evgeni Malkin scored against backup goalie Alexandar Georgiev in the third period.

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