Paul Millsap had 21 points and 11 rebounds, and Elton Brand, a fill-in starter at center, had 20 points and 11 boards for the Hawks, who have lost seven straight.
Trevor Ariza and Bradley Beal each had 19 points for the Wizards, who snapped a three-game losing streak.
Washington ended an 11-game skid in Atlanta, winning for the first time since Jan. 11, 2008.
The Hawks, who trailed by 20 points in the first half, made a third-quarter charge to twice cut the deficit to one point.
Ariza made the shot of the game to end the third quarter — a 57-footer from near the free throw line on the other end of the floor.
The Wizards moved a half-game ahead of Atlanta in the battle for fifth place in the Eastern Conference.
The Hawks had only nine players in uniform. Gustavo Ayon, who had been the fill-in starting center, was held out after hurting his right shoulder in Tuesday night’s loss at Indiana. Guard DeMarre Carroll missed his third straight game with a left hamstring strain.
Brand, 34, who has averaged 16 minutes as a backup, started at center, where the Hawks have a severe shortage of players. They already have lost All-Star Al Horford for the season after he had surgery to repair his torn right pectoral muscle. Horford’s backup, Pero Antic, is out indefinitely with a stress fracture in his right ankle.
Wizards center Marcin Gortat took advantage of the Hawks’ lack of size, scoring 14 points with 12 rebounds. Martell Webster had 13 points.
NOTES: Washington had seven players score in double figures. ... Ariza made five 3-pointers. ... Kyle Korver made his first 3-pointer of the game late in the first half, extending his NBA record to 122 consecutive games with a 3. ... G Cartier Martin, also making his fourth start, filled in for Carroll and scored only four points.