Williams moved from small forward to power forward and showed he can play big when needed.
Williams hit a go-ahead three-pointer with 26 seconds left and matched his career high with 14 rebounds, and the host Hawks overcame Caron Butler's 32-point effort to beat the Washington Wizards, 91-87, last night.
Williams scored 21 points to help the Hawks end a four-game losing streak.
"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 (Maryland, Calvert Hall) and Nick Young missed shots for Washington. Flip Murray then stretched the lead with two free throws for Atlanta with 10 seconds left.
"We're just not closing games out," Jamison said.
The Wizards have lost three straight and are 1-8.
DeShawn Stevenson sank a fall-away jumper with 1:32 remaining and added another basket less than 30 seconds later to give Washington an 87-83 lead.
Joe Johnson, who had 19 points, eight assists and eight rebounds, answered with a three-pointer for Atlanta with 57 seconds left to cut the lead to a point.
Washington's shot-clock violation with 32 seconds remaining set up Williams' go-ahead three-pointer.
Horford and Smith sat with ankle injuries.
Pistons 96, Cavaliers 89: Allen Iverson had 23 points and Rasheed Wallace added 21 as host Detroit ended Cleveland's eight-game winning streak. The Cavaliers' LeBron James shot 8-for-21 from the field and scored 25 points.
Mavericks 96, Rockets 86: Jason Terry scored 31 points to help Dallas win at Houston. Mavericks guard Josh Howard was inactive because of a left ankle injury, and Rockets center Yao Ming missed the game with a sore left foot.
Kings 105, Hornets 96: John Salmons scored 29 points and Bobby Jackson had all eight of his in the final 5:10 to help injury-hampered Sacramento surprise host New Orleans. The Kings played without guard Kevin Martin and forward Mikki Moore.
Nuggets 91, Spurs 81: Chauncey Billups scored 22 points, Carmelo Anthony (Towson Catholic) added 21 and surging Denver beat host San Antonio, still playing without injured guards Tony Parker and Manu Ginobili.
Clippers 108, Thunder 88: Cuttino Mobley had 12 of his season-high 23 points in a 23-4 third-quarter run that carried Los Angeles to a win at Oklahoma City. Mobley added a career-high seven steals.