Atlanta overcame a 2-0 deficit in the second period by scoring the last five goals in the contest, with three of them coming before the second intermission.
Vyacheslav Kozlov had a goal and an assist; Eric Boulton and Jean-Pierre Vigier each scored once while goaltender Kari Lehtonen made 25 saves for Atlanta (23-18-6), which has a club record five straight victories and beat the Stars for the first time in franchise history in nine games.
The Stars have lost two straight after a six-game winning streak. Dallas out-shot Atlanta, 27-21.
On the power play, the Stars went 2-for-5 while the Thrashers were 1-for-6.