The Bulls, who trailed by as much as 14 in the first half, momentarily took the lead in the fourth. They then fell behind by nine before making another run.
Rose scored the tying basket in regulation, then hit two free throws with 10.8 seconds left in overtime to seal it, sending the Bulls to their second straight win.
The Hawks had a chance to tie it, but Johnson missed a 3-point attempt. Rose got the rebound and missed two free throws with 2.3 seconds left, but Chicago's Joakim Noah blocked an outlet pass after Al Horford grabbed the rebound to secure the victory.
The missed free throws aside, Rose was at his best despite needing a cortisone shot for pain in his right rib cage. The Bulls would like him to assert himself, and he did just that, burying 14 of 24 shots.
Luol Deng chipped in with 21 points and 12 rebounds. John Salmons scored 16 and Chicago rallied again after falling behind by 17 in a win over New York on Thursday.
That was enough to offset a big effort by Johnson, who finished two points shy of his career high. Horford had 15 points and 12 rebounds, Jamal Crawford scored 14, but the Hawks simply couldn't put away Chicago.
Salmons' corner 3-pointer gave Chicago a 97-94 lead. Atlanta's Josh Smith then scored down low before a driving Deng shoveled the ball to Rose for a layup that made it 99-96 with 59 seconds remaining.
Johnson then hit two free throws to pull Atlanta within one, and Deng charged into Smith with 19.8 seconds left, but Johnson missed on a layup after driving by Salmons. Noah tipped the ball away as it bounced off the rim, Luol Deng got the rebound and Rose made it a three point game with two free throws.
It was a sharp turnaround for the Bulls, who looked like they were going to be blown out by Atlanta for the second time in 10 days. Even after they fell behind in the fourth, the Hawks looked like they were in good shape.
But Kirk Hinrich nailed a 3-pointer with 2:36 left in regulation to pull Chicago to 88-86, and the Bulls eventually tied it at 92 on Rose's driving layup with 35 seconds left after Johnson missed a jumper.
Johnson, who scored 12 in the fourth quarter, had another chance to give the Hawks the lead but missed a short fadeaway with 22 seconds left.
Deng grabbed the rebound, and after a full timeout and 20-second timeout, eventually missed an 18-footer off the dribble as time expired.<
NOTES: A three-time All-Star with an expiring contract, Johnson wasn't offering any clues about where he might wind up next season. "Anything's possible," he said. "I don't know what's going to happen. As of right now, I'm going to have fun." The Hawks are off to one of their best starts, so staying put is an option. Chicago also could be a major player in free agency. ... Hawks F Joe Smith missed his fifth straight game with a dislocated left thumb. ... Bulls F Tyrus Thomas will likely participate Sunday in some contact drills for the first time since he broke his left forearm in early November and could return after Christmas. Coach Vinny Del Negro does not expect him to play Monday against Sacramento or Tuesday in New York. The Bulls' next game after that is Dec. 26 against New Orleans.