Hinrich buried six big free throws down the stretch and Teague had a couple of costly turnovers as the Bulls held on for a 107-103 victory at Atlanta on Tuesday night.
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.
"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.
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.
Warriors guard Stephen Curry provides an update on how his injured knee is progressing.
Golden State's Klay Thompson gets off to a hot start in Game 1 against Portland by scoring 18 points in the first quarter. The Trail Blazers only tallied 17 in the opening frame.
Trail Blazers guard Damian Lillard drives to the hoop but is denied by Warriors forward Draymond Green with authority.