Griffin missed a 3 for Georgia, but Anne Marie Armstrong got the offensiverebound and scored with 8.5 seconds left in regulation to force the extra session.
When Jackson missed a more conventional shot, Nick Collison grabbed the offensiverebound and found a cutting Kevin Martin for a layup that turned into a three-point play and a 79-67 lead with 8:36 remaining.
The Nets completely wilted under the Heat's pressure, letting guard Mario Chalmers grab an offensiverebound while seated on the court, and throwing one inbounds pass away when there was no Miami player anywhere near to apply pressure.
But the run ended abruptly when George hit a 3, Miami's Joel Anthony was called for a loose ball foul on the offensive end and David West grabbed an offensiverebound and scored on a dunk to extend the lead to 77-68.