The Nationals used an error by Marlins first baseman Gaby Sanchez to load the bases with none out in the 10th, and Desmond lofted a deep fly to center field off Edward Mujica (0-1), easily scoring Wilson Ramos with the game-winning run.
Desmond also blasted a solo shot halfway up the left-field bleachers at Nationals Park in the sixth inning as the National League East-leading Nats continued their best start since 1981.
Jayson Werth also homered and Tom Gorzelanny (1-0) earned the victory with a scoreless top of the 10th.
Washington starter Stephen Strasburg tossed six scoreless frames without surrendering a walk and striking out eight.
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