Strasburg (3-0) allowed two runs, one earned, on five hits with three walks. Washington ended a three-game losing streak.
Rick Ankiel added a home run in the ninth.
Ryan Mattheus and Tyler Clippard each threw a perfect inning of relief for Washington and Henry Rodriguez survived a ninth-inning error to pick up his seventh save.
The loss went to Kevin Correia (1-3), who gave up six hits and both the sixth-inning homers.
The game was the only one on the National League schedule Thursday.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged