Cam York scored his first NHL goal, and Carter Hart made 24 saves for the Flyers (13-17-7), who are 0-5-2 in the past seven games.
The Rangers finished 3-2-0 on their road trip, which included four games against the Pacific Division in eight days. They flew home from San Jose on Friday.
"The long flight yesterday, the guys had 5 1/2 hours [on the plane], you get in at 7 o'clock in the evening, come all the way back here and then playing the next day," New York coach Gerard Gallant said. "They played hard, they played a good, consistent hockey game, they played for 60 minutes, and I was really proud of everyone tonight. We competed and we played well, and everybody chipped in."
The Flyers took a 2-1 lead at 10:11 of the third period on York's goal. Fox tried to clear the puck but it bounced off the boards to York, who one-timed it past Shesterkin. The rookie defenseman was playing his eighth NHL game.
"I knew that guys were going to be going to the net and I wanted to get a shot down there," York said. "Whether there was a rebound or not, we had bodies down there, so I just wanted to get it on net and luckily for me it went in."