The Kings scored the final two points in the fourth period on free throws by Ben McLemore with 17 seconds left and they then took a 98-94 lead in the overtime.
Sacramento, however, went scoreless over the final 3:59 while the Clippers were pulling away to win their fourth in a row.
Blake's dunk came with 2:03 remaining to give Los Angeles a 100-98 lead.
Jamal Crawford scored 31 points to lead the Clippers and Griffin had 21. The game was close throughout with neither side holding more than a seven-point cushion.
DeMarcus Cousins scored 25 points for the Kings, who have dropped three straight.