After the Shock (5-5) rallied to pull within 52-48 with 5:58 to play, Johnson hit a jumper, grabbed a defensive rebound and assisted on a layup by Milton-Jones to make it 56-48 just 53 seconds later.
Johnson, who shot 6-of-14 from the field, added another jumper with 3:44 remaining to push the lead to 58-49. Chasity Melvin scored 12 points and grabbed nine rebounds and Coco Miller chipped in 10 points in 18 minutes off the bench for Washington, which never trailed in winning on the road for the second time in five games.
Deanna Nolan was the only Shock player in double figures with 16 points. Detroit has lost four straight and five of its last six games since a 4-0 start. Overall, Detroit shot 35 percent (19-of-54) and made just 16-of-28 free throws.