George supplied 28 points and eight rebounds, and Hibbert added 24 and 11 as the Pacers came up big while facing elimination in the Eastern Conference finals.
The two teams will now play a winner-take-all contest Monday in Miami.
Indiana outscored Miami 29-15 in the third period to grab control of the contest and then turned back a Heat charge in the fourth quarter.
Miami, which had cut the deficit to four points at one point, was trailing 77-68 when Hibbert drew an offensive foul against LeBron James, resulting in technical fouls being called on James and Heat assistant coach David Fizdale.
George sank the ensuring free throws and the Pacers cruised the rest of the way.
James finished with 29 points, seven rebounds and six assists for Heat.
Celebrity Families of 2014 [PHOTOS]