The Panthers spotted Atlanta a 2-0 lead in the first period but fought their way back, tying the contest at 2-2 on David Booth's goal at the 10:45 mark.
That's how it stayed until White one-timed a pass from Peverley from the left circle past Florida goalie Scott Clemmensen for a 3-2 lead at 7:33 of the second. Pavel Kubina's sixth goal of the season with 5:13 left in the second gave Atlanta an insurance marker.
The Thrashers' Jonas Hedberg then stopped 13 shots in the final period to preserve the win.
Booth had a goal and an assist while Stephen Weiss chipped in with a goal for the Panthers.