Williams moved from small forward to power forward and showed he can play big when needed.
Williams hit a go-ahead 3-pointer with 26 seconds left and matched his career high with 14 rebounds, and the Hawks overcame Caron Butler's 32-point effort to beat the Washington Wizards 91-87 on Wednesday night.
Williams scored 21 points to help the Hawks snap a four-game losing streak.
Hawks coach Mike Woodson noted Williams also defended Washington's Antawn Jamison, who had 18 points.
"He was huge tonight," Woodson said. "To have to defend Jamison and still to be able to score 21 points and get 14 rebounds, that's a man's night."
Mike Bibby led the Hawks with 25 points, including 15 in the third quarter.
After Williams' go-ahead jumper from the right wing gave Atlanta an 89-87 lead, Juan Dixon and Nick Young missed shots for Washington. Flip Murray then stretched the lead with two free throws for Atlanta with 10 seconds left.
"It's the same situation," Jamison said. "We're just not closing games out. We're making the same mistakes. We've played it over and over again."
The Wizards, who have lost three straight, have only one win.
"We can't lose games like we did tonight," Jamison said. "We have to stop the bleeding. We have to find a way to win."
The Wizards were in position to win in the final minute.
DeShawn Stevenson sank a fall-away jumper with 1:32 left and then added another shot from the corner less than 30 seconds later to give the Wizards an 87-83 lead.
"We didn't give up when we were down by four with a minute left," Bibby said.
Joe Johnson, who had 19 points, eight assists and eight rebounds, answered with a 3-pointer for Atlanta with 57 seconds left to cut the lead to a point.
"They made some big-time shots," Washington coach Eddie Jordan said. "They played some pretty good defense down the stretch. ... Give them credit. Their defense did the job."
The Wizards' shot-clock violation with 32 seconds left set up Williams' go-ahead 3-pointer.
Butler made four 3-pointers for Washington. Stevenson had 12 points.
Zaza Pachulia, who filled in for Horford at center, scored only four points but set a career high with 18 rebounds.
"When Al is out there, he's always grabbing rebounds," Williams said. "Somebody has to do it. I guess it was me and Zaza's time."
The Hawks out-rebounded the Wizards 58-40 and claimed a 22-7 advantage in second-chance points.
Woodson was more impressed with his team's improved defense after allowing 113 or more points in three straight losses.
"That's just not us," Woodson said of the poor defense in the losing streak. "We were never really in those games, I don't think, from a defensive standpoint. ... I think our defense was back to where it was in the first six games of the season."
The Hawks opened the season with six straight wins before the four-game losing streak.
Bibby's big third quarter helped the Hawks rally from a 50-44 halftime deficit.
Bibby, who made only 1 of 5 shots from the field for 8 points in the first half, had 9 points in the final 3 minutes of the third quarter. The Hawks entered the final period with a 70-67 lead.
"The shots were open," Bibby said. "Guys were getting me open and finding me. I was just shooting what was there."
Butler helped keep the Wizards close with a long 3-pointer at the end of the third quarter, and he hit back-to-back 3s to give Washington a 79-75 lead with 5:40 left.
NOTES: Horford was held out because of a sprained right ankle. Pachulia was the fill-in starter at center. ... Smith, the starting power forward, missed his seventh straight game because of a sprained left ankle and could miss another four or five games, according to Woodson. ... Wizards rookie C JaVale McGee made his first start. He had five points and five rebounds. ... Jamison was scratched below his right eye with 32 seconds left but remained in the game.