Wheeler allowed the puck to slip away from his stick as he skated toward the goal in the shootout and Brian Boucher gave up on the play. Wheeler, however, regained control and fired home the shot that clinched the Atlanta win.
The Thrashers won for the fourth time in six games and have defeated the Eastern Conference's top club twice in the last five days.
Atlanta took a one-goal lead on three occasions Thursday, with scores coming from Tim Stapleton, Bryan Little and Nik Antropov. Danny Briere scored twice for the Flyers, running his total for the season to 31, but he missed his attempt in the shootout.
The win went to Ondrej Pavelec, who made 21 saves. Boucher stopped 22 shots for the Flyers.