The Lightning celebrated their season and home opener with a win thanks to Stamkos' first two goals of the year. His 51 tallies in 2009-10 tied Pittsburgh's Sidney Crosby for the league lead.
The game also marked Steve Yzerman's debut as the Bolts' general manager and that of Coach Guy Boucher.
The Thrashers were led by Ben Eager, who notched a goal and an assist.
Chris Thorburn and Tobias Enstrom added a goal each in Atlanta's loss.