Strasburg (3-5) -- in his third straight quality outing after suffering through a seven-start winless spell in April and May -- held the Phillies to one run and didn't allow a walk in the 112-pitch performance.
Washington broke open a scoreless tie with five runs in the seventh, highlighted by Steve Lombardozzi's two-run double into the right field corner.
Denard Span and Tyler Moore each added an RBI for the Nationals, who took the rubber match of their three-game series.
Phillies starter Cole Hamels (1-8) absorbed his fifth loss in five outings, surrendering five runs (three earned) on six hits in a 6 1/3-inning effort.
Notable deaths of 2014 [PHOTOS]