"I think he's going to be fine," Woodson said. "I think he just sprained his thumb, the one he had surgery on. But we'll treat him tomorrow, and I'm sure he'll be ready to go on Friday."
Atlanta also escaped a major scare when X-rays of Bibby's left thumb came back negative. Bibby left in the fourth quarter and didn't return, but trainer Wally Blase said the ninth-year point guard had a strain and would be listed as day-to-day.
The Hawks, winners in five of seven, remained a half-game ahead of ninth-place New Jersey, which beat Indiana on Wednesday night.
Bibby stayed in the game after driving the lane in the third and taking a hit from Milwaukee's Dan Gadzuric. Woodson wasn't surprised that Bibby, who finished with 16 points and three assists, tried to keep playing.
"Right now it's do or die," Woodson said. "We're trying to make the playoffs. That was kind of the conversation last night, how are these guys going to respond on a back-to-back? They responded because they want to make the playoffs as much as I do."
Bibby, acquired in a trade last month with Sacramento, missed the Kings' first 36 games after surgery to repair a torn ligament in the same thumb.
With home games Friday against Chicago and Sunday against New York, Atlanta needs Bibby in the lineup. The Hawks have missed the playoffs nine straight years, but Bibby helped Sacramento advance to the postseason for five straight seasons, ending in 2006.
"I was just thinking of us getting a victory, [but now] I may have to step in and start for this team," Atlanta rookie point guard Acie Law said. "You learn from a guy like Mike, the way the offense flows and how much better things run on the floor."
Johnson's 3-pointer at the shot-clock buzzer made it 45-43 midway through the second to give Atlanta its first lead since 4-2.
The Bucks, 6-29 on the road, never came within 10 points of the lead after Royal Ivey's 19-footer made it 94-84 early in the fourth.
Williams' right arm appeared to hit Bogut's nose on an inbound pass from the baseline. Bogut lay underneath the basket briefly before walking to the bench with a bloody nose.
"I'm not sure if my nose is broken or not, but after X-rays we'll fine out," Bogut said. "I wanted to get back on the floor, but obviously with all the blood, I couldn't do that. Had the game been close, I probably would have, but it made no sense at that point."
Michael Redd finished with 20 points for Milwaukee, which has lost seven straight on the road. The Bucks' leading scorer with a 23.3 average, Redd had 19 in the first quarter, but he was just 0-for-3 in the final three periods.
"It's really kind of hard to explain," Redd said. "I wasn't any less aggressive. It just didn't work out after the first quarter."
The Hawks were coming off a loss at Chicago on Tuesday, and Woodson could tell they lacked concentration on defense as Milwaukee, the NBA's No. 22 scoring team, trailed 65-60 at halftime.
"I thought the second half we really capitalized on our defense," Woodson said. "We shared the basketball and got stops when we needed to."
Johnson was 11-for-17 from the field, and Childress went 7-for-11. ... Atlanta is 5-11 against the Central Division, 5-3 at home. ... Milwaukee dropped to 8-8 against the Southeast. ... Bucks reserve forward Bobby Simmons missed the game because of the flu.