The Celtics owned a 15-13 lead before Utah got a lift from Marvin Williams, who scored five straight points and helped the Jazz regain a 24-22 lead.
Utah, however, managed only two points from their final six possessions and Boston took a 28-26 advantage into the second quarter.
The Celtics extended their lead to 34-27 with 10:50 left in the half before Gordon Hayward exploded. He scored 11 points during a 17-2 run that enabled Utah to build a 44-36 lead.
Boston answered with an 8-0 run to tie the game, but the Jazz converted their final five possessions to grab a 53-48 lead at the half.
In the third quarter, the Jazz own a 60-53 lead when Williams failed to convert on a fast break. On the other end, Bradley buried an open three-pointer, triggering a 10-0 that gave Boston the lead.
The Celtics extended their advantage to 80-72 heading into the fourth quarter, where the Jazz rallied behind the play of Hayward and forced overtime on Alec Burks' layup with 19 seconds left.