The Pacers had a four-point lead and the ball with 21 seconds to go in the fourth period, but George Hill missed 3-of-4 free throws down the stretch to keep Cleveland's chances alive. The Cavaliers then forced the extra period when Lester Hudson hit a jumper with a second to play.
Indiana dominated the overtime, however, to win its second in a row and inch closer to wrapping up a post-season berth. A loss by the Pacers would have allowed Chicago to clinch the Central Division title.
Granger scored 23 points and David West added 19 for the Pacers. Hill contributed 17.
Cleveland was led by Antawn Jamison with 21 points, but the Cavaliers could make just 3-of-21 from 3-point range.