With the game tied 1-1 less than 2 minutes into the second period, Stamkos stole the puck in the Capitals' end, outraced the defense on a clean break and slid the puck past Washington goalie Tomas Vokoun.
Tom Pyatt also scored for the Lightning and Mathieu Garon made the 2-1 advantage hold up the rest of the way, earning the victory with 23 saves.
Vokoun finished with 23 saves and Brooks Laich scored as the struggling Capitals lost for the ninth time in 13 games.
Missing from the Washington lineup was defenseman Pavel Kubina, who has reportedly been traded to the Philadelphia Flyers for a pair of draft picks.
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