Sim's shot past Johan Holmqvist gave Atlanta the shootout advantage. Kari Lehtonen deflected Erric Perrin's shot to clinch the win.
Atlanta's first-round playoff opponent will be the New York Rangers. As the Southeast Division champions, Atlanta is the No. 3 seed and the Rangers are the No. 6 seed.
In order to win the No. 6 seed in the Eastern Conference, Tampa Bay needed to beat the Thrashers and have the Rangers lose in regulation to Pittsburgh on Saturday.
Instead, the Lightning are the No. 7 seed and will face the New Jersey Devils.
Brad Richards and Vaclav Prospal scored in the shootout for Tampa Bay. Ilya Kovalchuk, who also scored in regulation, and Keith Tkachuk scored for Atlanta.
There was a delay in the shootout when Atlanta's Eric Belanger missed on a shot and broke the glass behind the net. The glass had to be replaced before Sim could take his shot.
Holmqvist stopped 39 shots in regulation and overtime. Lehtonen stopped 34 shots before the shootout for Atlanta.