Sue Bird added 12 points for the Storm (9-20).
Washington led by as many as 13 in the first half and Natasha Cloud's layup with 5:11 left in the third quarter gave the Mystics (16-12) a 10-point lead. The Storm scored the next 19 points, as the Mystics went scoreless for 8 minutes, 20 seconds, to make it 57-48 with 6:24 to play.
An 11-5 run pulled Washington within three with 2:34 left, but Seattle made 7 of 8 free throws from there to seal it.
The Storm shot 91.2 percent from the line, setting season highs for both free throws made (31) and attempted (34).
Ivory Latta scored 12 points for Washington, which hasn't won in Seattle in its last 10 tries, dating to July 13, 2005. Emma Meesseman and Kia Vaughn added 10 apiece.