Burmistrov fooled Scott Clemmensen with a nifty move in front of the net, firing the puck past him for the tie-breaker lead, and Thrashers netminder Ondrej Pavelec then made it hold up by stopping Cory Stillman.
The shootout win capped a stunning comeback for Atlanta, which trailed 2-0 with 1:58 left in the game. That's when Bryan Little and Chris Thorburn scored only 44 seconds apart to forge a tie.
Pavelec stopped 38-of-40 shots, including four in the scoreless overtime period, helping Atlanta to break a four-game skid.
Dennis Wideman and Dmitry Kulikov scored and Clemmensen turned aside 28-of-30 shots as the Panthers saw their three-game winning streak snapped.