Toronto tied it at 77 on a pair of free throws by Gay less than a minute into the fourth but, even with James on the bench, Miami answered immediately.
Gay made two free throws and added a jumper to put Toronto up 93-89 with 3:35 left, but New York tied it again when Anthony hit a pair from the line and Smith followed with a step-back jumper.
After the timeout, the Grizzlies got their lead back up to seven before Durant sandwiched a pair of driving buckets around Fisher's 3-pointer in a 7-0 burst that tied it at 84 with 3:47 to play.