Shesterkin made 18 saves in the first period, when the Rangers were outshot 18-9.
"I thought the first period they had us and we needed Igor to be really good, and he was," New York coach Peter Laviolette said. "He gave us a chance. ... We're a little slow out of the gate, and if he's not ready then it can be a different story. But he was on point tonight."
It was Shesterkin's sixth straight victory and third straight game allowing only one goal. He has a 1.84 goals-against average and .951 save percentage during his winning streak. It's a big difference from his previous 10 games, when he had a 3.25 GAA and .863 save percentage.
When asked what has changed, Shesterkin said with a laugh: "It's a secret. Nothing (has changed). Everything is the same, puck is the same size, I see the puck, same speed. Everything's the same, but the guys play awesome in front of me. I just start to touch the puck more, that's it."
Rempe put the Rangers ahead 2-1 at 6:31 of the third period, getting his first NHL point in his fourth game. The rookie forward was standing in front of the net when a puck redirected by Barclay Goodrow deflected in off his leg.
"Maybe the ugliest first goal in NHL history, but I'll take it," Rempe said. "It was so much fun. ... I felt something hit my shin pad pretty hard. I didn't know it was the puck, but I'll take it. Just go to the net, bang bodies, that's my game. Play fast and hard."
Shesterkin preserved the lead when he stopped Travis Sanheim with his left pad on a 2-on-0 short-handed breakaway at 10:10.
"He's incredible," Lindgren said of Shesterkin. "Both our goalies are, but 'Shesty' has been outstanding lately. He's keeping us in games, especially early. It seemed like they had a strong push from the start and Shesty kept that game at 0-0. He's been huge."
Lafreniere gave the Rangers a 1-0 lead at 11:56 of the second period. With the teams playing at 4-on-4, Vincent Trocheck skated the puck into the Flyers zone and passed to a trailing Lafreniere, who moved to the top of the left face-off circle and beat Ersson between his pads.