Strasburg (6-9), in his fourth major league season, made his 68th career start and needed just 99 pitches to subdue the Phillies.
The Nationals swept the three-game series to climb within three games of the .500 mark.
Strasburg had gone five starts without a victory, having last won on July 7 against San Diego.
A Philadelphia error led to two unearned runs in a three-run sixth.
Kyle Kendrick (10-9) gave up 11 hits and four earned runs in 4 1/3 innings to take the loss.
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