Byfuglien scored at 1:30 of overtime to give the Thrashers a 2-1 victory Sunday, extending the reeling Islanders' losing streak to 13 games.
The Islanders have their longest winless streak since playing 14 straight without a win Feb. 13-March 15, 1990. That streak included three ties.
The 6-foot-5, 265-pound Byfuglien drilled a powerful shot between the circles past Rick DiPietro.
"I was looking to pass, but I had a shot, saw it and took it," Byfuglien said.
The Islanders have only 12 goals in their last 11 games.
"We had several chances to win," New York's Matt Moulson said. "We have to score goals. ... You can't take comfort in getting just one point."
DiPietro, who had allowed 17 goals while losing his last three starts, made 33 saves and held the Thrashers to one goal in regulation.
"He was our best player," New York interim coach Jack Capuano said. "He was outstanding. He was what I thought he was going to be."
DiPietro couldn't stop the winner by Byfuglien, the playoff star for the Chicago Blackhawks last season who leads the NHL with four winning shots this season.
"I'm not sure what happened," DiPietro said. "He made a nice shot."
Thrashers coach Craig Ramsay said Byfuglien flourishes with the game on the line.
"He wants to be a difference-maker all the time," Ramsay said. "That's the biggest asset a hockey player can have ... is to want to be the difference-maker, to want to be the guy, to be the man. He puts his hand up."
Byfuglien also had an assist. He has seven goals and 19 points.
The Islanders (4-12-4) haven't won since opening the season 4-1-2.
"It's unacceptable for us," DiPietro said. "We need to win games. There are no excuses. ... It's frustrating, because we know what we're capable of doing."
The Islanders are 0-3 since Scott Gordon was fired as coach. New York has been outscored 10-4 in two games under Capuano, the former AHL coach, and 48-18 during the losing streak.
Byfuglien said goalie Ondrej Pavelec deserved credit for the win.
Pavelec stopped 28 shots, including a lunging glove save to his left late in regulation.
"We had to win it for him," Byfuglien said. "He kept us in the game."
Pavelec has allowed one goal in two straight wins, including a 5-0 shutout at Washington on Friday night. He has made a strong recovery after fainting in front of the net early in the opening game Oct. 8 and sustaining a concussion.
"I feel really good in the net and comfortable," Pavelec said. "It is a team effort. ... The guys in front played great tonight."
Michael Grabner knocked in a deflection in front of the net with only 13 seconds remaining in the second period to give the Islanders a 1-0 lead.
Nik Antropov's power-play shot from the right circle tied it early in the third period.
Jim Slater was denied on his chance to give Atlanta the lead with 6:17 remaining in regulation. Slater skated behind the net and attempted to score by wrapping his stick around the post, but DiPietro made the stop. A video review confirmed the call on the ice.
New York defenseman Mike Mottau was helped off the ice in the first period after he was hit by a puck, leaving a bad cut above his right eye. Mottau did not return.
- The Thrashers outshot the Islanders 14-6 in the scoreless first period.
- The Islanders were 0 for 4 on the power play, leaving them 0 for 24 in their last six games.
- Attendance was 10,066.