New York's winning streak is its longest since it won six straight from April 1-11, 2024.
"They're all a little different," Palmieri said. "I think it's really believing in each other and the way we need to play. Sometimes it takes a little bit to get there, but we've just been finding ways to get up and be on top when the final buzzer hits."
Ivan Fedotov made 25 saves for Philadelphia (23-24-6), which lost for the fourth time in five games and had a four-game home winning streak end.
The Flyers were coming off a 5-0 loss at the New Jersey Devils on Wednesday and have scored one goal or fewer in four of their past five.
"We're trying," Philadelphia forward Travis Konecny said. "We're getting some good looks. Obviously we've got to get some more traffic to the net. But also sometimes when we are there, the bounces are maybe just going the wrong way for us. We're pushing hard, guys are trying."
With the game 0-0, Flyers forward Matvei Michkov had a power-play goal overturned at 14:05 of the first period after the Islanders challenged for goaltender interference. It was determined Morgan Frost made contact with Sorokin in the crease.
Holmstrom gave the Islanders a 1-0 lead 10:02 of the second period when he scored from the high slot. It was the forward's fourth goal in five games.
Gatcomb made it 2-0 at 17:08 with his first NHL goal in his seventh game. After the Flyers were caught on a line change, Kyle MacLean and Gatcomb skated in on a 2-on-0 that Gatcomb finished.
"I was ready for it, but at the same time I thought [MacLean] was going to shoot," Gatcomb said. "He faked the goalie pretty well, and me a little bit there. So you’ve just got to be ready at all times."