Both players held break point opportunities in the second set, before Djokovic broke in the final game with a forehand winner.
Simon then made a bright start to the final set, breaking for 1-0 and conceding just two points in the first two games.
But Djokovic levelled at 3-3 when Simon made a backhand error, and the Frenchman had to fight off another break point before holding for 4-4.
Djokovic then held for 6-5 on his third game point, and broke for the match after Simon set up match point by netting a low forehand volley. The relieved Serbian closed out the match with a smash.
"I was one set up, I was playing far better than him, because he made so many mistakes from the baseline," said the frustrated Simon.
"I had enough chances to win this match, and finally I lost it, so that's why it is a very bad match."
In Delray Beach, Florida, top-seeded Mardy Fish reached the Delray Beach International quarterfinals with his easiest win yet over fellow American Vince Spadea 6-4, 6-1 on Thursday. The duo has been playing each other for nearly a decade, but this was the first match between the former Delray Beach finalists to finish in two sets.
"We've always had tough matches," Fish said. "I think I've figured out what to do."
Fish made sure of it with two breaks in the second set. He's hoping to become the first top seed in the 17-year history of this tournament to claim the winner's trophy.
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