It was the second straight year Woods closed with an eagle at PGA National — the difference was last year, it gave him a 62 and a tie for second.
"I think I passed 62 somewhere around 12," Woods said.
Despite a bogey on the final hole, Erik Compton had a 70 and was part of the five-way tie for fourth. Compton, who already has had two heart transplants, earned his first top-10 finish on the PGA Tour.
Thompson finished at 9-under 271, a strong performance considering the difficult course and the weekend wind. He was among three players who never shot over par at PGA National.
"You don't have to do much wrong to be making a bogey out there, so it's pretty impressive," Ogilvy said of Thompson's final round. "It's a great effort, really. As you say by the rest of the scores, it's a very hard golf course and it seems to get progressively harder in some ways. There's a disaster waiting everywhere.
"There's a lot of golf courses on tour that it might be easy to close out a golf tournament — or easier — but this is not one of them."
Thompson was at his best in the middle part of the final round.
He hit a tough chip off the pine straw to 3 feet for par on the 10th, and then hit flawless chips for easy par on the 11th and 14th holes to build a four-shot lead. Not even the late run by Ogilvy was enough to stop him.
"This is everything," Thompson said. "This is a childhood dream come true. I've dreamed of playing out here since I was 7 years old and to win, it's just unbelievable. I just can't put it into words. The whole day was awesome."