Johnson's two-run homer into the right-field seats came in Atlanta's three-run sixth inning off Doug Fister (1-1). Fister gave up 10 hits and five runs, four earned, in 5 2-3 innings.
The Nationals committed four errors, including two by Fister on errant pickoff attempts.
The losing streak is Washington's longest since six straight from July 19-24, 2013.
Stults (1-1) allowed two runs on four hits and three walks. Johnson had three hits, including a run-scoring single off Rafael Martin in the seventh.
