After stopping all 18 shots in regulation and overtime, Ilya Bryzgalov was beat by Nielsen on a fake to the backhand that was lifted high.
Danny Briere, playing in his first game after missing six contests with a concussion, deked to the forehand and tried to stuff it in, but Evgeni Nabokov stuck his left pad out to the post and kept the puck out.
Nabokov stopped 45 shots through the 65 minutes of play for his second shutout of the season and 52nd of his career for the Islanders, who have won three of four.
"When you look at the game, he made some huge saves for us," said New York head coach Jack Capuano. "Anytime you get goaltending like that, normally you win a hockey game and we did that tonight against a really good team."
Bryzgalov posted his second shutout of the season and 25th of his career, but it wasn't enough to prevent the Flyers from losing three straight for the first time this season.
"We didn't score tonight," said Philadelphia head coach Peter Laviolette. "There was traffic there at times, but not always. You are cycling the puck and you need bodies to cycle the puck. You can't do it with one man. There were opportunities where we did have guys, it just didn't go."
The Isles halted a 13-game losing streak in Philly with a 4-1 win on January 19 thanks to 40 saves from Nabokov. He was up to the challenge again on Tuesday as he stopped 10 shots in the first period, 15 in the second and 16 in the third before overtime saw him stop four shots to force the shootout.
He had to be on his toes all game as his team was thoroughly outshot every period as his counterpart needed to stop just seven each in the first two periods and had to make just four saves in the final 25 minutes.
Each team has won twice in the season series...Both squads went 0-for-3 on the power play...Philadelphia hosts Toronto on Thursday...The Islanders play host to the Canadiens on Thursday...The Islanders and Nielsen agreed to a new contract on Tuesday. The team confirmed the deal, which will be officially announced on Wednesday and it is being reported that it is for four years and $11 million.