Strasburg (15-5) won for the sixth time in seven decisions, dominating the Braves on one run over six innings. The right-hander allowed four hits and walked one while raising his major league-best strikeout total to 183.
Drew Storen and Sean Burnett each hurled a scoreless relief frame and Tyler Clippard racked up his 28th save for the National League East-leading Nationals, who clinched their three-game series with second-place Atlanta.
Danny Espinoza belted a three-run homer and Ian Desmond added a solo shot as Washington won for the fifth time in six games.
Atlanta's Paul Maholm (11-8) was touched for four runs on seven hits in a seven-inning effort.
Freddie Freeman provided the only RBI for the NL wild-card-leading Braves.