NEW YORK — Teammate J.T. Miller looked at Carl Hagelin and shook his head in admiration.

“The guy is at his best in games like that,” Miller said.

A game like Friday night’s fifth match between the Rangers and Pittsburgh Penguins that Hagelin won 10:52 into overtime, moving New York into the second round of the Eastern Conference playoffs. The Rangers won the series 4-1, with each victory by a 2-1 score, the last two in OT.

Hagelin skated out from behind the net and put a wrist shot on the short side behind Marc-Andre Fleury, who was equally as brilliant as Rangers goalie Henrik Lundqvist. Hagelin’s teammates stormed off the bench, while Fleury lay on the ice, despondent.

“It’s unbelievable,” Hagelin said. “One of the coolest things I’ve ever experienced on the ice. An unbelievable feeling.”

The Rangers will play the winner of the Washington-New York Islanders series, which the Capitals lead 3-2. Rather than look ahead to which opponent they might face, the Rangers looked forward to a few days off.

“The rest is definitely beneficial,” defenseman Marc Staal said, noting the Rangers needed seven games in each of their first two series last year on their way to the Stanley Cup Finals. “It’s not something that our group is used to, but it’s definitely a nice change of pace.”

New York also won Game 4 in Pittsburgh in OT on Kevin Hayes’ goal, on which Hagelin assisted.

Lundqvist made 37 saves in Game 5, including a nifty stop on Brandon Sutter in the extra session that was wide open, a bit sloppy, but very entertaining.

“It was a one-goal game every game,” Lundqvist said, “so the difference between the wins and the losses here was some big plays by some great players. Luckily for us, we had the extra effort there to pull off the wins.”

The Rangers had the NHL’s best record, finishing 15 points ahead of the Penguins in winning the Presidents’ Trophy. But they were pushed all series by Pittsburgh, a team they had never beaten in the playoffs until storming back from a 3-1 deficit last year in the second round.

“Unfortunately, we’ve been on the wrong side of these 2-1 games for a few,” said Sidney Crosby, who managed only four points in the series. “Small margin for error, so it’s hard to really absorb it right now. Tonight we could have easily been going back to Pittsburgh down 3-2, but again we were on the wrong side.”

New York’s problematic power play opened the scoring. Dan Boyle’s weak shot from the point fooled Fleury, who knocked it down — directly to Derek Stepan in front of him. Stepan put home a tap-in just 3:23 in.

Moments later, on Pittsburgh power play, Lundqvist made a brilliant save on Evgeni Malkin. Lundqvist also was fortunate that Nick Spaling’s deflection that got through the goalie trickled wide.

Fleury was just as strong at the other end after the early goal. He stuck out his glove to thwart a deflection by Miller that was ticketed for the net.

Both goalies kept up the stinginess in the second period. Whether it was Fleury denying Derick Brassard on successive shots, then making two saves while down on the ice, or Lundqvist making outstanding stops against Paul Martin, Brian Dumoulin and Patrick Hornqvist, the session belonged to the netminders.

Until Spaling tied it on a weird goal. Crosby centered from the side of the net and the puck bounced in the air with traffic in the crease. It went in off Spaling’s arm, making it 1-1.

Crosby, who drew a penalty — and the Garden fans’ ire — when he flopped over behind the net while trying to work the puck loose from Dan Girardi, hit the right goal post on that power play. Crosby was loudly booed the rest of the night whenever he touched the puck.

Moments later, it was the Rangers’ turn to hit iron when Miller’s steal led to his shot caroming off the crossbar. Then Boyle was robbed by Fleury’s pad on a backhander before missing an unguarded net off Miller’s feed seconds later.

And it was on to overtime. And then, it was on to the second round for the Rangers.

“It’s good that we answered here in the first round,” Staal said, “and we were able to close out a pretty good hockey team.”

Notes: Rangers F Mats Zuccarello left in the first period with an undisclosed injury. He appeared woozy as he slowly skated to the bench, and the team had no update afterward. ... Pittsburgh was 2 for 13 on power plays in the series, the Rangers went 3 for 20. ... Malkin had no points in the series.