Kyle Korver had 16 points and Jeff Teague added 13 as Atlanta (15-7) won for the third time in three meetings with the Wizards (3-19) this season.
Former Hawks draft pick Jordan Craword had 27 points, 11 rebounds and 11 assists to lead the Wizards. Nene scored 18 points, Bradley Beal had 17 and Martell Webster 11.
After Washington took a 93-92 lead on a jumper by Earl Barron with 3:05 to play in overtime, the Hawks scored six straight points to go up five with 1:29 to play.
Williams hit one of two free throws to tie the score, and Stevenson hit a 3-pointer with 2:08 left to put Atlanta back ahead for good, 96-93. After he made the shot, the former Wizard turned toward the booing crowd, waving his hand in front of his face.
Stevenson and Al Horford each made free throws, and Crawford hit a jumper with 48 seconds left to pull Washington to 98-95.
Nene had a jumper blocked by Smith with 9 seconds to play, and Korver made two free throws to cap the scoring.
Barron scored his first basket of the game with 23 seconds left in regulation to tie it at 90. He missed his previous eight field goals.
With the score tied at 58-all, Beal went up for a dunk. Smith blocked it, and Beal fell hard to the floor, stayed motionless for a few moments and left the game with 5:29 to play in the third quarter. A minute later, Beal left the floor with trainer Eric Waters.
Without Beal, the Hawks ran off a quick seven straight points on a 3-pointer and a dunk by Teague and another dunk by Smith. Beal returned to the bench a few minutes later. After three quarters, Atlanta led 72-69.
The Hawks led through nearly the entire first half with a 52-46 advantage at halftime. Beal was 6 for 7 from the field and had 12 points in the opening half.
NOTES: Stevenson made a dunk late in the third quarter. His previous 25 baskets had been 3-pointers. His last 2-pointer came nine games ago on Nov. 21 against the Wizards. ... Atlanta G Anthony Morrow missed his second straight game with a sore back. ... Washington F Trevor Ariza, who has missed the last seven games with a sore left calf is improving, coach Randy Wittman said, and he hopes to have him back next week. ... The Hawks host Oklahoma City tonight. The Thunder are 20-4 and have won 11 straight games.