Stamkos, assisted by Martin St. Louis, got the game-winner at 2:56 of the extra session.
Stephane Veilleux, Ryan Malone and Kurtis Foster scored for Tampa Bay in regulation and St. Louis ended up with three assists.
Antero Niittymaki blocked 28 shots in a win that improved his record to 14-0-0 against the Thrashers.
Slava Kozlov, Tobias Enstrom and Evander Kane scored for Atlanta, which has lost three straight games after winning four in a row.
Thrashers goalie Ondrej Pavelec had 36 saves.
Copyright 2009 by United Press International.
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