Strasburg (8-9) had been 0-3 in his previous five starts, losing his last three outings. He walked one and didn't permit a runner past second base.
The NL East-leading Nationals split the four-game series after dropping the first two to the last-place Phillies.
Denard Span had two hits, two steals, an RBI and scored a run for Washington.
Cole Hamels (6-6) allowed an unearned run over seven innings. The left-hander gave up four hits and struck out six in his second consecutive start without an earned run. He has given up one earned run or fewer in nine of his last 13 starts.
The Phillies were shut out for the second straight day and haven't scored in 21 innings.
Cody Asche got two hits for the Phillies, but also committed an error at third base on Jose Lobaton's chopper that led to Washington scoring in the third inning.
After dropping the ball, Asche grabbed it and his wide throw pulled first baseman Ryan Howard off the bag. Strasburg sacrificed and Span hit a looping single into right-center.
After Asche's two-out double in the fifth, he appeared to be picked off on Lobaton's throw from behind the plate to shortstop Ian Desmond. Second base umpire Tripp Gibson's safe call stood after a review of more than three minutes, prompting a chorus of boos from the home crowd.
Phillies: Left fielder Domonic Brown has an infection in his tonsils and will see a doctor in Philadelphia on Monday. He was out of the lineup for a third straight game. ... Right fielder Marlon Byrd batted fifth despite continuing to battle a bruised right foot. Byrd's last off day came Tuesday at the Mets.
Phillies: After an off day Monday, Kyle Kendrick (5-11, 4.92) makes his seventh career appearance (five starts) against Houston on Tuesday. It will be Kendrick's first start against the Astros since they joined the American League.
Nationals: Washington welcomes Baltimore on Monday in a makeup of their July 8 rainout. Tanner Roark (11-6, 2.74) will make his first career start against the Orioles.