Time was running out on a season of unexpected success for the Rangers. They were losing by a goal and the anxiety was rising at Madison Square Garden. A terrific run seemed to be over.

But all season long, including in the previous two games of the playoffs, the Rangers found a way to claw back to win, and on Sunday they did it when it mattered most, in the most dramatic fashion.

Trailing by a goal with less than six minutes to play in regulation, Mika Zibanejad rifled a wrist shot to tie the score. Then 4 minutes and 45 seconds into overtime Artemi Panarin, scored on a wrist shot on the power play to win Game 7 of their first-round playoff series, 4-3, and send over 18,000 fans at the Garden into delirium.

It has been a season in which the Rangers exceeded expectations and tantalized fans with their future potential. But the one unknown was playoff experience and the ability to win on the biggest stage.

They certainly have that now, and it will be useful when the Rangers take on the Carolina Hurricanes in the second round of the playoffs.

The Rangers, who faced a three-games-to-one deficit, recorded their first series win since 2017, while the Penguins lost their first Game 7 on the road after winning their first six in franchise history.

“We’ve been a resilient group all year long and that didn’t change in the series,” Chris Kreider, the Rangers winger, said in a television interview after the game.

Leading in to the game, there was a good deal of anticipation about whether Sidney Crosby would play. It had been four days since Jacob Trouba knocked him out of Game 5 with a crunching check, with Trouba’s left elbow making contact with Crosby’s face. Trouba was not penalized on the play, and although it initially looked intentional, replays of certain angles indicated he might have had his elbow up high as he played the puck close to Crosby’s feet.

Crosby, who has missed 115 games with concussions in his 17-season career, went down from the blow. Soon after, he left the game for good, and did not play in Game 6, which the Rangers won, 5-3, in Pittsburgh. There were reports before Sunday’s Game 7 that Crosby was not diagnosed with a concussion and may have been kept out of the lineup for precautionary reasons.

About a half-hour before Sunday’s game, a murmur went through the arena when Crosby skated onto the ice for warm-ups. Crosby is considered a villain to Rangers fans, in part because of a reputation that he falls easily to the ice to draw penalties, and they demonstrated little sympathy for his ailment, chanting his name with derision.

But there is little doubting his skill and leadership, as the winner of three Stanley Cups, two regular-season most valuable player awards, two playoff M.V.P. awards, and multiple scoring trophies. He was also the most threatening player for the Penguins in the first four games of the series before his injury.

Crosby buzzed the ice with conviction from the beginning on Sunday, set up teammates with penetrating passes and forced Rangers goalie Igor Shesterkin to make a stretching glove save off a slap shot in the first period. He assisted on Jake Guentzel’s goal in the second period for his 201st playoff point, tying him with Jaromir Jagr for the fifth most in N.H.L. history.

Crosby was also the focus of a skirmish near the Rangers’ goal late in the first period when he tried to pry the puck away from Shesterkin. The Rangers did not appreciate that, and Rangers defenseman Ryan Lindgren pounced on top of Crosby, which caused a small ruckus and resulted in matching penalties.

The Rangers scored midway through the first period when Zibanejad and Kreider stormed down the ice for a two-on-one breakaway. Zibanejad, streaking down the left wing, passed across the ice to Kreider, a left-handed shooter, who set up from the right face-off dot and drilled a one-time slap shot over the left shoulder of Tristan Jarry that hit the crossbar and went into the goal, eliciting an emphatic celebration from Kreider.

It was Kreider’s fifth goal of the series and third in the last two games, and Zibanejad’s seventh assist. For Jarry, it was a nearly impossible shot to stop, and one of the first he had seen in game action in a month.

Mike Sullivan, the Penguins’ coach, made a calculated gamble when he assigned Jarry to start the game. Jarry had not played since April 14 because of an injury, believed to have been a broken bone in a foot. Louis Domingue, a third-string goalie, played in the first six games for Pittsburgh, entering in the second overtime period of Game 1, and was mostly solid. But the last goal Sullivan saw slip past Domingue was not a great play for the goalie. Kreider’s game-winning shot from the point with 1 minute 28 seconds left in Game 6 struck off Domingue’s padding, bounced over his head and behind him into the goal.

Jarry is considered a better goalie, but there was no guarantee that his reflexes would be sharp. Sullivan, though, has never been afraid to make high-risk, high-reward moves.

With time running out in the first period, the Penguins evened the score on a goal by Danton Heinen, which was only credited to the Penguins after a replay review. The teams traded goals in the second period, too, as Guentzel scored for Pittsburgh and K’Andre Miller evened the score for the Rangers.

But later in the period, Evan Rodrigues scored a remarkable backhand goal on a breakaway as the Penguins took a 3-2 lead into the second intermission, and the tension mounted toward a gripping conclusion.