Capitals goaltender Tomas Vokoun made a great stop on Martin St. Louis after he and Stamkos broke in on net during the extra frame, but Stamkos was there to poke in the loose puck for the game-winner, his NHL-leading 33rd goal of the season.
Both he and St. Louis notched goal and an assist while Mathieu Garon finished with 26 saves as the surging Lightning won their fifth straight.
Mathieu Perrault, Matt Hendricks and Troy Brouwer scored for Washington, which dropped its third game in four contests.
Vokoun ended with 27 saves for the Capitals.
2014: The Year in Music [PHOTOS]