The Bulls survived a dramatic contest that brought them their third straight victory.
It was close throughout the second half with Boston taking a three-point lead on two free throws by Kevin Garnett with 20 seconds left in the fourth period.
Hinrich could make just 1-of-2 from the line for the Bulls with 12 seconds to go, but Chicago's Joakim Noah stole the ball from Paul Pierce and that set up a jump shot by Hinrich with 2 seconds left that forced overtime.
The Bulls then scored first in the extra period and the lead changed hands six times after that.
Boston moved in front by a point with 12 seconds to go on a jumper by Jason Terry, but Belinelli answered with a turnaround fadeaway shot. A 3-point attempt by Boston's Courtney Lee failed to go at the buzzer.