Johnny Oduya had two goals for the Thrashers, who have won three of four and nine of 11 overall. Bryan Little and Anthony Stewart also lit the lamp.
Chris Mason, making his first start since November 14, stopped 25-of-29 shots to take his first win since November 3.
Rob Schremp and Blake Comeau each had a goal and two assists for the Islanders, who have lost five in a row and 19 of their last 20 games. Matt Moulson had a goal and an assist for New York, which also got a goal from Matt Martin.
Rick DiPietro turned aside 30-of-35 shots in defeat.
With the score tied at three, the Thrashers went in front on a crazy short-handed goal. The referee dropped the puck for a faceoff at the right circle and Little quickly fired the puck into the upper right corner of the net past a shocked DiPietro with 8:25 to play.
Evander Kane had a chance to increase the margin but was stopped on a penalty shot at the 14:12 mark, but the visitors were able to make it 5-3 on the ensuing faceoff. The Thrashers won a right-circle draw and Brent Sopel’s shot from the point was deflected in by Burmistrov.
New York scored a rare power-play goal to make things interesting. Comeau, positioned in front of the net, took a pass from Schremp and chipped the disc past Mason with 1:16 remaining. It was the Islanders’ first man-advantage score in 47 chances.
Atlanta was then able to hold off the home team with the net empty in the final minute.
New York scored the lone goal of the first period at the 16:53 mark. After Atlanta turned the puck over at its own blue line, Comeau fired a shot on net from the slot. The puck sailed wide and hit off the backboards, but Martin was in a perfect position at the side of the net to jam the disc past Mason.
Moulson’s goal at the 2:44 mark of the second stanza made it 2-0, but Stewart found the back of the net with 1:59 left to start Atlanta’s comeback.
Oduya scored a pair of goals early in the third to put the Thrashers ahead. At the 5:45 mark, Oduya controlled the puck at the point and carried to the slot before beating DiPietro with a wrister.
Atlanta took the lead at 7:03 when Oduya lit the lamp again. Nik Antropov slid a pass to the slot for Oduya, who somehow wristed a bouncing puck into the back of the net to make it 3-2.
The Islanders tied the game just over two minutes later. Andrew MacDonald’s shot from the left point set up a rebound in front for Schremp, who chipped the puck past Mason.
Atlanta has won three in a row against the Islanders, including both meetings this season…The Thrashers started a three-game road trip on Saturday by winning on Long Island for the first time since December 23, 2008…Atlanta went 0-for-5 on the man advantage.