Game 7 is Sunday in Atlanta.
Carlos Delfino scored 20 for the Bucks, who came into the game hoping to finish off their heavily favored opponent but instead went completely flat coming out of halftime. The Hawks outscored the Bucks 29-11 in the third quarter to take a 15-point lead.
Milwaukee made a furious comeback attempt in the last 6 minutes, cutting the lead to 7 with just over 5 minutes left, but Josh Smith's block on John Salmons with just over 2 minutes remaining helped stop the rally and the Hawks pulled away.
Al Horford had 15 points and 15 rebounds for Atlanta.
It was an off night for two of the Bucks' top offensive threats, Salmons and Brandon Jennings.
Jennings scored 12 points on 4-for-15 shooting, including 1 of 9 from 3-point range. The rookie missed his first six shots and made questionable decisions with the ball after playing well through most of the first five games of the series.
Salmons finished with eight points on 2-for-13 shooting.
The Hawks got what they needed off the bench from Crawford, the NBA's sixth man of the year. He had been stuck in a shooting slump for much of the series but was better Friday, hitting 8 of 17 from the field. His late layup helped the Hawks take the air out of the Bucks' late rally.
Milwaukee's Jerry Stackhouse - who brought down the house by singing a soulful rendition of the national anthem before the game - made a 3-pointer, and the Bucks turned it into a four-point play when Kurt Thomas was fouled and hit a free throw.
Two more free throws by Stackhouse cut the lead to seven with 5:14 left, but Johnson hit a jumper and Crawford drove for a layup to put the Hawks back up by 11. Jennings answered with a layup, and Johnson missed a layup.
Jennings then missed a 3-pointer and Salmons got the rebound, but Smith forcefully blocked Salmons' shot and the Hawks couldn't rally from there.
Milwaukee led by three at the half, and Delfino hit a driving layup to begin the third quarter.
But the Bucks went silent for nearly eight minutes from there, allowing the Hawks to go on a 19-0 run that included a steal and fast-break slam dunk by Smith, who fired up the crowd by posing and holding his hand to his ear.
Smith has been booed relentlessly by Bucks fans after joking early in the series that there wasn't anything to do in Milwaukee.
Milwaukee wasn't expected to do much in this series, having lost its best all-around player, center Andrew Bogut, to a gruesome arm injury near the end of the regular season.
Atlanta took a 2-0 series lead, and the Bucks weren't particularly competitive in either game. But then the series shifted back to Milwaukee, the Bucks asserted themselves on defense and won both games - then stole Game 5 in Atlanta with a late run.
NOTES: Stackhouse surprised the crowd by grabbing the microphone before the game and singing the national anthem to raucous applause - so much so that whatever he yelled to fire up the crowd afterward couldn't be heard. ... Smith had 10 points, nine rebounds and four blocks. ... Friday was the 39th anniversary of Milwaukee's 1971 NBA championship.