The 76ers stunned the Bulls in six games just as it appeared Chicago would be able to extend the opening-round series to a deciding seventh contest on its home court. Instead, Omer Asik missed two free throws for the Bulls with 7 seconds remaining and then fouled Iguodala, setting up the game-winning points.
Iguodala blocked a 3-point attempt at the buzzer by C.J. Watson to clinch Philadelphia's first playoff victory in nine years.
Chicago's hopes of advancing deep into the post-season and, perhaps, to the NBA title were extinguished with the loss of 2011 league MVP Derrick Rose to a knee injury in the opening game of the series. Joakim Noah sat out the final three games of the series with an ankle injury.
The deflated Bulls lost the second, third and fourth games of the series, but fought back to win Game 5 and came close to capturing Thursday's contest.
Chicago overcame an eight-point halftime deficit and took a three-point lead when Asik scored on a dunk with 25 seconds to play. Thaddeus Young then made a layup to bring the 76ers within one with 12 seconds to play and Asik was fouled by Spencer Hawes.
The 7-0 Asik, who had made 4-of-5 from the line during the game, suffered two critical misses and followed that misfortune by putting Iguodala in a position to win the game.
Iguodala scored 20 points and both Jrue Holliday and Lou Williams had 14 for Philadelphia.
Richard Hamilton and Luol Deng both scored 19 for the Bulls, whose 50 regular-season victories were tops in the Eastern Conference.