West, an undrafted rookie from Georgia Tech, had not played more than 8 minutes in a game, but he had 4 points, 2 rebounds and a steal in the first 7 minutes.
"Mario West was a big key for us," said rookie Al Horford, who had 12 points. "He really got that energy going early in the game."
The Hawks broke open a close game with a 13-2 run midway through the fourth quarter, including six points by Childress. Atlanta outscored Milwaukee 23-14 in the final quarter.
"In the second, third and fourth quarters our defense really settled in," Woodson said. "I thought we were as good defensively as we've been all year."
The Bucks lost for the second straight night following a five-game winning streak.
"Atlanta did a nice job attacking," said Bucks coach Larry Krystkowiak. "We had a hard time keeping the ball in front of us, because they broke us down off the dribble consistently. It was the type of attack we expected, we just weren't ready to move our feet."
The Bucks call their top five reserves the Bomb Squad, but against the Hawks the backups fizzled, making only 2 of 18 shots. Charlie Villanueva, Charlie Bell and former Hawks guard Royal Ivey combined to go 0-for-12.
"Our bench normally provides a big spark for us, but tonight they struggled, which I think hurt us," Krystkowiak said.
Atlanta outscored Milwaukee 24-14 in the second period to lead by 16 late in the first half at 50-34, but cold shooting by Josh Smith helped open the way for Redd and Williams to lead Milwaukee's comeback. The Hawks' lead was only 3 points in the final quarter before the 13-2 run.
Smith was only 4-of-14 shooting for 10 points, but Redd said the Bucks couldn't make up for their sluggish second quarter.
"The second quarter really destroyed us," Redd said. "Next thing I know, we're down by 10 at halftime. We kept trying to make a run, but it was just too much of a task."
Redd and Williams combined for 16 of Milwaukee's first 18 points of the third quarter as Atlanta's 67-54 lead was cut to 67-63. Smith made a long jumper and then stole a pass to set up a layup by Pachulia, and the Hawks led 73-66 entering the final quarter.
A steal and basket by Williams, followed by a 17-foot jumper by Redd, cut Atlanta's lead to 73-70. Two free throws by Bobby Simmons again cut the lead to 3 at 75-72 before the Hawks used a 13-2 run that began with a 3-pointer by Lue.
Childress capped the run by grabbing an offensive rebound to set up his own basket with 5:05 left for an 88-74 lead.
Smith, who set a career high with 38 points in a loss at Milwaukee on Nov. 17, had only 4 points on 1-for-6 shooting in the first half. Still, the Hawks led 52-42 at the halftime break as Johnson and Horford combined to make 8 of 12 shots for 22 points.
Milwaukee's only bench points came from Simmons (5) and Dan Gadzuric (2). ... Atlanta won only for the fourth time in its last 13 games against Milwaukee. ... Williams was held out with a strained right hip after starting the first 13 games. He could return on Friday. ... Hawks rookie PG Acie Law IV plans to practice Thursday and may return from a left ankle injury Friday against New Orleans.