Casey Cizikas scored his first goal of the season, and Brock Nelson had a goal and an assist for the Islanders (12-13-6), who are 5-1-1 in their past seven games.
"Standings are tough to look at," Cizikas said. "You can look at them one way and kind of be upset, or you just take it game by game, and I think that's what we're doing here. Each game is the most important game of the year to us right now, and at the end of the season, if we keep playing the way we are, we keep growing as a group and playing the way that we are, then we're going to like where we're sitting."
Travis Konecny scored for the Flyers (13-18-7), who went 0-for-4 on the power play and are 0-6-2 in their past eight games. Martin Jones made 27 saves.
The teams will play again at Philadelphia on Tuesday.
"Honestly, I thought we played pretty well tonight," Jones said. "We were able to get in on the forecheck and spend more time in the [offensive] zone, which was great. Defensively, I thought we were pretty good. We were pretty strong in our own end. We didn't really give up many odd-man rushes.
"We're right there. We just need to find a way to win right now."
Sorokin kept the game scoreless when he stretched out his right pad to deny Scott Laughton on a 2-on-0 with Konecny 46 seconds into the second period.
"I just [focused] on the puck," Sorokin said. "I waited until the player shot or made a pass, and he made a shot in the middle of the net and I was in position."
Nelson gave New York a 1-0 lead at 11:44 of the second with a wrist shot from the edge of the left face-off circle after receiving a drop pass from Josh Bailey.
Cizikas made it 2-0 at 14:28, redirecting Robin Salo's wrist shot from the point. It was his first goal since April 1, 2021.
"It's been a long time coming, to be honest with you," Cizikas said. "When I turned around and I saw [Matt Martin's] hands in the air, honestly I thought it hit him and went in. It's definitely a good feeling and something to build off of going into tomorrow night and the rest of the year."
Konecny cut it to 2-1 when his attempted cross-ice pass deflected in off Islanders defenseman Noah Dobson at 17:12.
Sorokin then had to make a save against Joel Farabee on a breakaway to keep New York in front with 58 seconds left in the period.
"You look at the second period, the chances that we had, I thought that we looked fast at different points of the game," Flyers coach Mike Yeo said. "We're working extremely hard for anything that we get right now, but there's still moments or times in the game where we just give up something too easily."
