The Pacers won in Chicago for the first time since March 2008, having lost their five previous trips to Illinois.
Chicago, which had a four-game winning streak snapped, trailed by four in the final minute. The Bulls' Brian Scalabrine missed a 3-point attempt with 29 seconds to go and Hibbert quickly slammed home the shot that wiped out Chicago's hopes.
It was only the fourth loss of the season for the Bulls, who have the best record in the Eastern Conference.
Danny Granger led Indiana with 22 points and Hibbert had 20. The Pacers have played five more road games than they have home contests.
Derrick Rose, in his second game since returning from a toe injury, had 24 points for the Bulls. Luol Deng missed his second contest with a torn ligament in his left wrist.