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.
Carney made another 3 with 1:59 to go and give the 76ers its first lead of the second half, 105-104. Louis Williams' layup extended lead to 107-104 with 1:00 left.
The Bulls had a chance to take the lead in the final 21 seconds but Chicago guard Larry Hughes was called for an offensive foul. Iguodala hit two free throws with 19.5 seconds left to make it 109-106.
Ben Gordon had a chance to tie it with 8.2 seconds left but missed a 3-point try.
Thabo Sefolosha added 20 points in a reserve role and Larry 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.
Sameuel 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.
