Iguodala made the go-ahead free throws with 2.2 seconds left, and Philadelphia rallied for a 79-78 victory over the top-seeded Chicago Bulls in Game 6 on Thursday night, advancing to the second round of the Eastern Conference playoffs for the first time since 2003.
The 76ers will face Boston, which beat Atlanta in six games, in the conference semifinals.
"I don't know how we won this game," coach Doug Collins said.
Collins and the Sixers hardly cared the series win comes with an asterisk.
The Bulls lost reigning MVP Derrick Rose to a torn anterior cruciate ligament in his left knee late in their Game 1 win. Center Joakim Noah missed the last three games with a sprained left ankle.
"I thought we had more than enough to win with," Bulls coach Tom Thibodeau said. "I'm disappointed in the loss, but I'm not disappointed in our team."
Without their stars, the Bulls found it tough to gut one out against the Sixers.
Omer Asik missed two free throws for the Bulls with 7 seconds left that would have given them a three-point lead. Iguodala grabbed the second miss, sprinted the length of the court, and was fouled by Asik on the driving layup.
The Sixers are the fifth No. 8 seed to win a first-round series against a No. 1 seed. Memphis eliminated San Antonio last season, while Golden State (2007), New York (1999) and Denver (1994) also pulled off the rare feat.
"We were on the ropes and we battled," Bulls forward Carlos Boozer said. "In the end, it came down to the very last second. So, it's tough. We were right there, given everything, right there. It will be a long summer."