Strasburg (4-1) coughed up three early runs (two of them unearned), but then settled down, ultimately allowing four hits over five innings while walking one and fanning eight -- giving him a National League-best 64 strikeouts.
The Nats began a comeback in the third inning when Strasburg led off with a single, Danny Espinoza doubled and Bryce Harper scored both on a triple.
Jesus Flores and Strasburg belted back-to-back solo homers in the next frame, putting the Nats up 5-3.
Espinoza and Ian Desmond each added a pair of RBI for Washington, which salvaged one win in its three-game interleague set against the Orioles.
Wei-Yin Chen (4-1) absorbed his first loss the season. He was lit up for six runs on eight hits in a 4 1/3-inning effort.
Xavier Avery went 2-for-4 with a run-scoring single for American League East-leading Baltimore.