The Hawks were without injured forward Josh Smith. Johnson and Jamal Crawford each had 12 points. Johnson had nine assists.
The Hawks cut Chicago's lead to 79-78 on a 3-pointer by Marvin Williams with 1:18 remaining.
Atlanta finally pulled even at 79 when Horford made one of two free throws. A free throw by Noah gave Chicago an 80-79 lead.
Following a timeout, Crawford drove toward the basket and passed to Horford, whose jam gave Atlanta its first lead at 81-80.
Chicago's Kyle Korver missed a 3-pointer at the final buzzer.
Horford had 13 points in the third quarter as the Hawks cut into Chicago's lead.
"He was a beast tonight," Drew said. "He did it all at both ends.
"In the huddles he was cheering the guys and telling them to keep playing. He was phenomenal."
Williams said Horford is at his best when playing against Noah, his former University of Florida teammate.
"Al would probably never admit it, but I think it's personal," Williams said. "You always want to bring it against your former [teammates], and he does it every time."
Horford said he tried to take up the slack for Smith, who had an MRI on his right knee during the game. Smith hurt his knee in Monday night's loss at Denver and the team said he sprained his medial collateral ligament.
"With Josh out, I felt like I had to step up my game a notch," Horford said.
Noah was impressed.
"Horford played great," he said. "It was an outstanding effort.
"It's a tough way to lose, but it just shows you've got to play the game for 48 minutes."
The Bulls established a physical and dominant pace when Noah beat Horford for the opening tip.
Rose penetrated and passed to Carlos Boozer, who dunked for the game's first basket. Noah blocked a shot by Horford on the other end, and the Bulls were on their way to the 14-0 run.
Johnson, guarded by Deng much of the game, missed seven of eight shots in the first half. He finished with 12 points on 5-for-20 shooting.
Chicago starters outscored Atlanta's first five 42-16 in the half for a 50-33 lead.
Kirk Hinrich had three points while making his first start in his third game with the Hawks. He was acquired in a five-player trade with Washington last week.
Tensions flared late in the first half when Horford was fouled hard by Boozer, who wrapped his arm under the All-Star center's chin. With Horford on his back under the basket, Hawks center Zaza Pachulia pushed Chicago players away. Horford remained in the game to make one of two free throws.
Chicago has lost six straight in Atlanta since its last win on April 1, 2007. ... The Hawks recalled G-F Pape Sy from Utah of the Development League. ... Jason Collins started for Smith. ... The Hawks went 8:48 without a field goal in the second quarter. ... Horford hit his first 3-pointer of the season and second of his career in the third quarter. His double-double was his 30th of the season.