Thompson seized control early with a 50-foot eagle putt on the third hole, then kept his distance with clutch par saves and closed with a birdie from the bunker. It gave him a 1-under 69 — one of only five rounds under par at PGA National — and a two-shot win over Geoff Ogilvy.

“This week was magical,” Thompson said. “Just had a groove and kept feeling it.”

It was a big week for Ogilvy, too.

The former U.S. Open champion had plunged to No. 79 in the world ranking and already missed the Match Play Championship. He was prepared for another week off next week until putting together four solid rounds.

He chipped in from behind the 16th green for birdie and two-putted for birdie on the 18th for a 69. The runner-up finish moves him into the top 50 (No. 47) and gets him into the World Golf Championship at Doral.

Luke Guthrie, tied with Thompson for the 54-hole lead, fell behind with a bogey on the second hole and closed with a 73 to finish third.

Tiger Woods was never in the picture.

He started the final round eight shots behind, and whatever hopes he had of a rally ended on the sixth hole when he hit his drive so far to the right that the ball was never found.

Woods took double bogey, and only an eagle on the final hole kept the damage to a minimum. He closed with a 74 — his first time since the Masters last year that he failed to break par in any round of a 72-hole tournament — and tied for 37th.

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, who finished at 9-under 271, had made only one cut this year and finished at the bottom of the back. He was solid from the start Sunday on another windswept day in south Florida, one of only three players who shot par or better all four rounds.

“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 dropped only one shot on the back nine, a three-putt on the 16th when he missed from just inside 3 feet. He rattled another short par putt in on the 17th, and then played away from the water on his second shot at the par-5 18th, into a bunker. Once his ball stopped rolling 4 feet from the cup, the tournament was over.

The win moves Thompson to No. 45 in the world and gets him into his first World Golf Championship next week.

“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.”

It was a mess for Woods.

He lost two balls in a span of eight holes (the other one in the third round Saturday) for what he believes is the first time in his career. He hit into the water on the 11th for another double bogey, and drove into the water on the 16th.

“I just made too many penalties this week,” Woods said. “Today is a perfect example. I didn’t play that poorly. I had two water balls and a lost ball. Take those away, and I missed two short birdie putts, and it was actually a decent score. So just got to clean up my rounds.”

The final round was never going to be easy with the wind whipping on PGA National, and it showed. Of those who finished before the leaders even teed off, only two players managed to break par. Scoring was so difficult that Lucas Glover played the weekend in 2-over par and still tied for fourth.

“You don’t move up very often — on tour — over par on the weekend, except for a place like this,” Glover said.

Thompson seized control early because of some big putts, and mostly because so many others faded.

It was a wild front nine for Thompson, with only three pars, which ordinarily would spell disaster on a day like this except for his putting.

He made a 50-foot eagle putt on the third hole, made a 12-foot birdie putt behind the hole at the par-3 fifth hole and hit an approach into 4 feet for birdie on the eighth. Just as big was the tough sixth hole, where Thompson hit a bunker shot 18 feet over the flag and made the par putt coming back.

Guthrie, who fell behind for good with a bogey on the second hole, did his best to stay in range until hitting his tee shot out of bounds on the 14th for a double bogey. From there, it was only a battle for second place.

Everyone else was long gone.

Westwood failed to save par on consecutive holes on the front nine and could never catch up. Charles Howell III, who started the day three shots behind and needed a win to get to the Masters in his hometown, fell apart on the back nine with a 41 and closed with a 78.

He at least gets into Doral next week through his FedEx Cup standing. Rickie Fowler made three bogeys on the first six holes and was never a factor.

Thompson’s short game was superb during the pivotal part of the final round. He twice chipped to tap-in range for par on the 10th and 11th holes, and he built a four-shot lead with four holes to play. The only thing that kept him from an easy walk to this first win was Ogilvy’s late birdies.