Both runners moved up on pitcher Chris Stammen's sacrifice bunt and scored when Desmond blasted a double high off the right-field wall.
Rookie phenom Bryce Harper smacked his first major-league homer while Xavier Nady and Chad Tracy also went deep for the Nationals, who with Atlanta's loss Monday regained their one-game lead atop the National League East.
Stammen (3-0) earned the win with two shutout innings of relief and Sean Burnett earned his first save to secure the victory.
Orlando Hudson knocked in a pair of runs for the Padres.
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