Philadelphia trailed 88-70 with 11:08 left, then outscored the Bulls 18-6. Carney hit a 3-pointer with 3:30 left and Iguodala hit another 3 at 3:11 to tie it at 98.
"What Chicago does inside their building is they usually get off to big starts. This is not unusual for them. We just hung in there and never stopped playing," Cheeks said.
Carney made another 3 with 1:59 to go and give the 76ers their first lead of the second half, 105-104. Louis Williams' layup extended the lead to 107-104 with a minute left.
The Bulls had a chance to take the lead in the final 21 seconds, but guard Larry Hughes was called for an offensive foul. Iguodala hit two free throws with 19.5 seconds left to make it 109-106.
"I was thinking, 'Can we really come back?' Coach said if we can just get it down to 10, but the guys have a lot of heart, we cut it, got some stops and before you know it we were up," Iguodala said.
Ben Gordon had a chance to tie it with 8.2 seconds left but missed a 3-pointer for the Bulls, who also blew a 20-point lead at home to the Wizards on Feb. 29.
"It's like we got caught in quicksand in the fourth quarter," said Bulls forward Drew Gooden. "Defensively they switched to a zone and they were effective."
Thabo Sefolosha added 20 points in a reserve role and Hughes had 15 points, five assists and seven rebounds for the Bulls, who trail the New Jersey Nets by one game for eighth place in the Eastern Conference.
Andre Miller scored 18 points for the 76ers after leaving in the fourth quarter of Wednesday's win in Detroit with a lower back strain. Philadelphia was 40-for-44 from the free-throw line.
Philadelphia came into the game last in the league in free-throw shooting.
"Coach has been really stressing about getting extra free throws and we've been shooting just about every day," Iguodala said. "I think we're last in free-throw percentage in the league so we've really been focusing in that area and it paid off tonight."
Samuel Dalembert had 11 points and nine rebounds for Philadelphia, which has won eight of its last 10 games.
The Bulls tried to pull away in the second quarter. Leading 32-30, Andres Nocioni made a 3 and Sefolosha went the length of the court to convert a three-point play. Sefolosha then hit a 3 on the Bulls' next possession and Aaron Gray finished Chicago's 11-2 run with a basket in the lane to give them a 43-32 lead with 5:50 left in the second quarter.
The 76ers cut the lead to 46-37 on Kevin Ollie's three-point play, but the Bulls answered with 11 straight points. Hughes scored seven points in the span and Luol Deng's basket gave Chicago a 54-37 lead with 2:26 left in the half.
"I thought we played well for stretches, really for about 36 minutes. We've had difficulty playing well for 48 minutes. That was especially tough giving that one away," Hughes said.
Philadelphia G Willie Green missed his second straight game with a lower back strain. Cheeks expects Green to play on Saturday against the Spurs. ... Chicago G Chris Duhon didn't see any time for the third straight game after missing a Bulls' shootaround on Sunday morning.