The Heat bounced back from a 100-76 home loss to the New York Knicks the previous night, also receiving the grim news that O'Neal needs surgery to repair torn knee cartilage. He will have the procedure on Sunday and be out four to six weeks.
On this night, Wade made sure the defending NBA champions didn't miss O'Neal.
"A lot more is going to come on me," Wade said. "Most of the time when he's playing, he may get 40 or 50 touches and I may get 40 or 50. When he's out, I get more."
Wade hit a jumper from outside the arc with 2:04 remaining in OT to tie the game at 81. After Tyronn Lue missed a 3 for the Hawks, Wade lured the defense toward him before dishing off to an open Williams, who made the long jumper with 1:31 left to put Miami ahead to stay.
"I saw he had a little room," Wade said. "I passed it to him, and he shot it in."
Wade made four straight free throws in the final 24 seconds to clinch it.
Atlanta, which started the season 4-1, lost its third in a row to fall back to .500. All three have been tight -- two in overtime, the other a two-point defeat. Joe Johnson led the Hawks with 22 points.
"The last three games were a carbon copy," Johnson said. "We can't close out games."
Miami nearly won during a wild final minute of regulation. The Heat had four chances for the go-ahead basket, outhustling Atlanta for three offensive rebounds, but Antoine Walker missed three jumpers and Wade failed on the other attempt.
Walker had an open 3 at the buzzer, but the shot caught the back of the rim as the horn sounded. The Miami player ran all the way to the other end of the court in disgust. Coach Pat Riley merely smiled in disbelief, the game going to overtime tied at 74.
Both teams shot miserably. Miami was only 36 percent (32-of-88) from the field, while the Hawks shot just 37 percent (33-of-89).
"It could have gone either way," Wade said. "They kept coming and we kept coming until it got to the point where we won the game."
Atlanta went more than seven minutes without a field goal late in the game. Lorenzen Wright dunked home an offensive rebound with 4:58 remaining in the fourth -- the Hawks' last basket of regulation. They finally broke the drought on Salim Stoudamire's 3-pointer with 2:44 left in overtime.
Wade scored 20 of Miami's 42 points in the first half, and he came through again at the end. He finished 11-of-25 from the field, made 14 of 17 free throws, doled out nine assists and grabbed seven rebounds.
"That's what they pay him for -- scoring and making plays," teammate Gary Payton said. "He did what he gets paid for. He did fine."
The Hawks were held to a season low for points in both the first quarter (12) and the first half, trailing 42-32 at the break. Atlanta finally went ahead for the first time in the third period and led 59-58 heading to the fourth.
"We've got to keep working hard, but it's hard when guys don't come out ready to play," Johnson said. "That hurt us tonight. That hurt us the last few ballgames. It's going to keep hurting us if we don't do anything about it."
The Hawks played without F Josh Childress, who sat out with a sprained left foot and was listed as day to day. ... Miami F Dorell Wright had an embarrassing moment in the fourth. After making a steal, he broke in all alone and attempted a spectacular dunk. There was only one problem -- the ball caught the back of the rim and bounced out, drawing jeers from the crowd. ... The Hawks announced another sellout, their third in five home games this season. ... Michael Doleac managed to pick up five fouls in just over 10 minutes of playing time. ... Payton banged up his left knee in the third quarter and didn't return. But he doesn't expect to miss any games.