Facing elimination, the Magic got better leadership from center Dwight Howard, who top scored with 32 points, and had more success unlocking Boston's tight defense.
Orlando let slip a 10-point lead midway through the second quarter, setting up a raucous final period. Guard Jameer Nelson helped secure victory with a pair of three-pointers in overtime.
The series shifts back to Orlando's home court on Wednesday, with the Celtics leading 3-1 in the best-of-seven series.
(Reporting by Ros Krasny; Editing by Peter Rutherford)