Noah Cates and Travis Sanheim scored for Philadelphia (36-29-11), which lost its fifth straight game (0-3-2). Fedotov made 19 saves on 21 shots in his NHL debut after replacing Samuel Ersson (four saves on six shots) at the start of the second period.
"I'm not a young guy (27 years old) and have some experience and know how it's working," said Fedotov, who joined the Flyers on Friday following the termination of his contract with CSKA of the Kontinental Hockey League. "I don't care if it's playing from the first minute or during the game. I need to play, so it doesn't matter. I just want to help the team. Give energy, emotion and that's it."
Cates gave the Flyers a 1-0 lead at 4:57 of the first period with a shot from the high slot.
Martin tied it 1-1 at 12:03, scoring off the stick of Flyers defenseman Egor Zamula after a clearing attempt by Scott Laughton was knocked down in the slot by Kyle MacLean.
Horvat scored his 30th of the season 18 seconds later to put the Islanders ahead 2-1. He beat Ersson blocker side from the left circle on a 3-on-2 rush.
Sanheim scored 43 seconds into the second period to tie it 2-2, skating the puck the length of the ice before beating Varlamov glove side off the post from the high slot.
"Not sure we really liked our game for the majority of it, but find a way to get a point," Sanheim said. "Unfortunate break in overtime."
Lee put New York back in front 3-2 at 17:54 of the second when he redirected Alexander Romanov's shot from the left point.
"This is a huge game for us to make up some ground," Nelson said. "Would have liked to do it in regulation, for sure, but to get the extra point, it's still something. ... We were approaching it like it was a do-or-die scenario for us, just given that this is a team specifically that we're chasing, couple games in hand. We need the points."
Philadelphia was outshot by New York 17-3 in the second period.
"Soft," Flyers coach John Tortorella said. "One guy played: the goalie.
"There are certain people, they don't have a clue how to play or just don't have it in them to play in these types of situations. And this is why I'm glad we're playing them, because we have to figure things out as far as what we're going to become as a team here. That was embarrassing, the second period for the Philadelphia Flyer uniform, the way we played. Embarrassing. High marks as far as how we came back in the third (outshot New York 19-3)."
NOTES: Nelson's goal was also his 30th, the third straight season he's reached the mark. He's the first Islanders player to score at least 30 goals in three straight seasons since Matt Moulson from 2009-12. ... Horvat's goal was his 500th point in the NHL. ... Varlamov has started three straight games for the first time since March 29-April 1, 2022. ... Flyers forward Sean Couturier left the game with 7:39 remaining in the first period after falling hard into the boards in the Islanders' zone. Tortorella had no update after the game. ... Drysdale had an assist and four shots on goal in 20:52 of ice time in his return after missing 16 games because of an upper-body injury.