Dunleavy also had eight rebounds and four assists. He was covered in ice bags as he sat slumped at his locker after playing all but nine seconds in the game.
"I appreciate (coach Tom Thibodeau) giving me that nine-second breather at the end of the half," Dunleavy said with a laugh. "That made a big difference."
The Bulls won after trailing by 14 points in the first quarter.
"They put us in a hole; we fought out of it," Dunleavy said. "We just had to battle the whole game."
Since Jan. 1, Chicago is 12-1 when holding its opponent under 90 points. No other team in the league has kept as many opponents under 90 in that span.
Teague had 26 points for the short-handed Hawks, who have lost nine of 10. Shelvin Mack scored 17.
The Bulls led most of the second half but never pushed the advantage to double figures.
"I think they really wanted that game today," Noah said of the Hawks. "We really wanted that game, too. It wasn't pretty at times. I'm just happy we were able to come out with the win."
DeMarre Carroll's fast-break basket gave Atlanta a 100-99 lead, but Dunleavy answered with a layup. With 1:03 remaining, Carroll sank a 3-pointer to give Atlanta a 103-101 lead.
With 43.2 seconds remaining, officials reviewed and confirmed a questionable foul called on Carroll on Hinrich's 3-point attempt. Hinrich made the three free throws to put Chicago in front again.
Noah's steal from Teague got the ball back for the Bulls with 20 seconds remaining. Atlanta's Kyle Korver stole the inbounds pass, giving the Hawks a chance to take the lead, but Teague stepped out of bounds behind the basket. Hinrich then made two free throws.
Noah stripped Mike Scott of the ball on Atlanta's next possession, setting up another foul shot by Hinrich. Coach Mike Budenholzer and the Hawks argued that Noah fouled Scott.
"Do I think he was fouled?" Budenholzer asked after the game. "I just looked at it, and yes I do."
Scott said Noah hit his arm but added "Can't do nothing about it now."
Budenholzer also protested Carroll's foul on Hinrich but said after watching the replay he agreed with that call.
Hawks All-Star forward Paul Millsap missed his second straight game with a right knee contusion and also will be held out on Thursday at Boston.
The Hawks also were without centers Pero Antic (stress fracture, right ankle) and Gustavo Ayon (right shoulder), who had filled in following Al Horford's season-ending torn pectoral muscle.
Budenholzer said morale isn't a problem.
"I thought our group competed at a very high level for 48 minutes tonight," Budenholzer said. "That's what we're looking for, and that's what is most important to us."
Korver hit 3-pointers on Atlanta's first two possessions, extending his NBA record to 125 straight games with a 3. Korver added a third trey a couple minutes later, and his strong start seemed to spark the Hawks, who jumped to a 26-12 lead.
Chicago closed the deficit with a 13-2 run in the final minutes of the opening period and start of the second quarter. The Bulls led 54-51 at halftime.
Mack sank a short jumper with about 2 seconds remaining in the third period. D.J. Augustin, who had 10 points, then banked in a half-court shot for Chicago, lifting the Bulls to an 80-75 lead heading to the final period.
NOTES: Glenn Frey of the Eagles, who played at Philips Arena on Monday night, had a second-row seat near midcourt. ... NBA Hall of Famer Julius Erving had a front-row seat and tipped his cap when called out by the P.A. announcer and cheered by fans. ... Bulls guard Jimmy Butler missed his second straight game with bruised ribs. ... Korver had 16 points and Carroll had 13.
Copyright by STATS LLC and The Associated Press
ATLANTA, GA - FEBRUARY 25: Jeff Teague #0 of the Atlanta Hawks drives against Mike Dunleavy #34 of the Chicago...
MVP: Joakim Noah, whose defense came alive in the fourth quarter, when he came away with three steals against the Hawks. He also had 20 points, 12 rebounds and three assists to go with those clutch takeaways.
Defining moment: With 14 seconds left and the Hawks down only one, Jeff Teague drove to the basket and appeared to have a step. However, the Bulls' defense recovered and forced Teague to the baseline, causing the Atlanta PG to turn the ball over by stepping out of bounds.
That was ... classic Thibs: Coach Tom Thibodeau has a rep for playing his starting small forward a lot of minutes, whether it be Luol Deng or Jimmy Butler. This time it was no different with Mike Dunleavy, who played all but nine seconds of this game.