The Mystics blew a 12-point second-half lead but regained it on the clutch shot by Schuman, who scored 14 points.
Detroit's Deanna Nolan missed a 3-pointer, and Washington's Chamique Holdsclaw sank six free throws in the final 40 seconds to seal the win. Holdsclaw scored 27 points, making 13-of-14 from the line.
Tamicha Jackson scored 14 of her 16 points in the first half as Washington grabbed a 44-33 lead. Chasity Melvin added 10 points and rookie Alana Beard pulled down 10 rebounds for the Mystics, who have won three of their last four games.
Swin Cash scored 23 points and Ruth Riley added 19 and nine rebounds for the Shock, who have lost twice at home to the Mystics this season. Nolan scored 11 points.