The 76ers will face Boston, which beat Atlanta in six games, in the conference semifinals.
Omer Asik missed two free throws with 7 seconds left that would have given the Bulls a three-point lead. Iguodala grabbed the second miss, sprinted the length of the court, was fouled by Asik and made both free throws.
The Sixers are the fifth No. 8 seed to win a first-round series against a No. 1 seed.
Chicago lost star guard Derrick Rose to a knee injury in the series opener and centre Joakim Noah didn't play in the last three games because of an ankle injury.
Iguodala scored 20 points, and Jrue Holiday and Lou Williams each scored 14 for the Sixers who were outrebounded 56-33.
Luol Deng had 19 points and 17 rebounds for the Bulls while Richard Hamilton scored 19 points and Carlos Boozer grabbed 13 rebounds.
CELTICS 83, HAWKS 80
BOSTON (AP) — Kevin Garnett had 28 points, including the jumper to give Boston the lead with 31 seconds left, and 14 rebounds as the Celtics advances to the Eastern Conference semifinals for the fifth straight year.
The Celtics will play Philadelphia, which eliminated East No. 1 seed Chicago in six games.
Garnett had five blocks and three steals for Boston, while Paul Pierce had 18 points despite playing with a sprained medial collateral ligament in his left knee, and Rajon Rondo had 14 points and eight assists.
Josh Smith had 19 points and nine rebounds for Atlanta, which failed to advance in the playoffs for the first time in four years. Joe Johnson had 17 points, Marvin Williams added 16 points and eight rebounds and Al Horford had 15 points and nine rebounds.
Horford missed the first of two foul shots with 2.3 seconds left after he was tackled by Marquis Daniels to avoid an easy dunk that would have tied the game. After he made the second, the Celtics got the ball to Pierce, he was fouled and made both free throws.
NUGGETS 113, LAKERS 96
DENVER (AP) — Ty Lawson scored 32 points and Corey Brewer added 18 as Denver forced a Game 7 in their first-round playoff series.
Game 7 in the Western Conference series is Saturday night at the Staples Center.
This will be the Nuggets' first all-or-nothing playoff game since losing to Utah in Game 7 of the 1994 conference semifinals.
Kobe Bryant followed his 43-point outburst in Game 5 with 31 points in 3 1/2 quarters despite a sour stomach that prevented him from attending the Lakers' morning shootaround and forced him to take intravenous fluids all day. He took a seat for good with Los Angeles down 101-73 with 7:52 remaining.
The Nuggets have won three of four since dropping the first two games in Los Angeles.
Andrew Bynum pulled down 16 rebounds but made just 4 of 11 shots for 11 points for the Lakers and Pau Gasol was just 1 of 10 from the field, finishing with three points and three rebounds.
Rookie Kenneth Faried had 15 points and 11 rebounds and Danilo Gallinari and Andre Miller both had 12 points for Denver, which led 90-68 heading into the fourth quarter.