Panarin cut it to 3-2 with a shot from the right circle that beat Ersson on the far side at 12:23, but Rodrigo Abols scored a short-handed goal off a 3-on-1 rush at 14:36 to give Philadelphia a 4-2 lead.
It was the Flyers’ first short-handed goal this season.
"We went in the second period without a goalie," Shesterkin said, blaming himself for the four goals allowed on 11 shots. "They were easy goals. I was upset, but I just tried to come back and give us a chance to win.
“We played so well in the offensive zone today. I owe dinner for everyone."
Shesterkin said the Rangers talked about belief while in the dressing room during the second intermission.
"Everyone went to the rink, stepped on the ice with the same mindset," Shesterkin said.
Trocheck sparked them by scoring off his own rebound to cut it to 4-3 at 9:13 of the third.
"That gave us a little more energy," Zibanejad said. "It's one thing to believe, but you've got to get something out of it too. You've got to get something to rally around it and get that energy, and we got that energy from that goal. That was huge for us. After that, you're trying to do everything in your power to get another one. And we did, so that was good."
New York tied it after Rasmus Ristolainen went to the box for a delay-of-game penalty at 17:00. Morrow set up Zibanejad for the one-timer.
"I've hit better one-timers than that and they haven't gone in," Zibanejad said. "At that time during the game, it's nice to see that one go."