The Flyers are 1-5 in shootouts this season and an NHL-worst 20-39 in their history.
Bryzgalov played well in the first 65 minutes and notched his 25th career shutout, but he struggled in the shootout. He is 0-4 in shootouts this season, having allowed eight goals on 10 shots.
"I think we play very well, but it's a bad taste in the mouth after losing in the shootout," said Bryzgalov, who suffered a loss while recording a shutout for the first time in his career. "Obviously, I've got to work on this kind of thing in the practice more."
The last time the Flyers were in a scoreless tie that reached a shootout was Dec. 6, 2005, when Antero Niittymaki and Calgary's Mikka Kiprusoff were the goalies. The Flyers won the shootout.
The Flyers' top line of Claude Giroux (6), Scott Hartnell (6), and Jaromir Jagr (4) combined for 16 of the Flyers' shots Tuesday.
Jagr, who was robbed on an early one-timer, said Nabokov was "reading the plays. He was there even before we tried to shoot. Even when we went give-and-go or a cross-ice pass, he was there. I don't know if he's that quick or he was reading it very well. He was good tonight."
"He made the saves that he had to, but we didn't put traffic in front of him," said Giroux, who would have been the third shooter had the shootout gone longer. "He likes to get his room. He challenged a lot of shots, and I think we kind of let him do whatever he wanted. I think we've got to do a better job of screening the goalie."
First periods have haunted the Flyers recently, so it was almost a moral victory that they were in a scoreless tie after the opening 20 minutes, outshooting the Islanders, 10-7.
It marked just the second time in their last nine games that the Flyers had outshot an opponent in the first period. They entered the night with just three wins in their last eight games - and had been outscored, 7-2, in the first periods of those five losses.
"We talked about being ready to play," coach Peter Laviolette said before the game.
But even with Briere back in the lineup after missing six games because of a concussion, the Flyers couldn't solve Nabokov.
In one of their best opportunities, Nabokov stopped Max Talbot on a backhander while the Flyers were killing a penalty late in the second period.
Nabokov, 36, made three saves against Jagr in the final 4 minutes, 46 seconds of the second, including a one-timer that he kicked away with his left pad, and a point-blank shot with 23 seconds to go.
The Flyers had entered the night with 23 wins over the Islanders in their last 25 meetings. The Isles, with Nabokov making 40 saves, scored a 4-1 win over the Flyers on Jan. 19, their first victory at the Wells Fargo Center since 2007.
Contact staff writer Sam Carchidi at firstname.lastname@example.org or @BroadStBull on Twitter.