Woods won for the third time this year by outlasting fellow American Bo Van Pelt in a back-nine duel that went down to the final hole.
"What an incredible week," Woods said.
"I remember there was a time when people were saying I could never win again."
Woods closed with a two-under 69, giving him a two-shot victory and moving him into second place on the tour's career list, one ahead of Nicklaus. He needs eight more to equal Sam Snead.
Woods, who finished at eight-under 276, took the lead on 17 where Van Pelt made bogey after his ball sailed over the green.
All Woods had to do was maintain the lead on the final hole.
He sealed the victory with a superb nine-iron approach that landed and rolled onto the flat part of the green on 18.
"It was downhill, the wind was hot and the ball was flying," said Woods, who also won at Muirfield Village and Bay Hill this year. "It fit my eye for some reason. I just saw it and hit it."
His win capped a bizarre week of golf at the Congressional Country Club course. A violent heat-fuelled storm wreaked havoc on the course, blowing down trees and forcing organisers to shut the course to spectators on Saturday, making for a peculiar scene as the golfers teed off without galleries.
"Yesterday was a silent day, but I think everyone saved it up for today," Woods said after the spectators were allowed back on the course on Sunday.
The clean-up operation was extensive and the players still had to navigate some small piles of debris, just off some of the fairways, that didn't get cleared in time for the final round.
"The staff, the maintenance crew and everybody. Yesterday was a very difficult situation. They worked their tails off to get it done," Woods said.
"Everybody, thank you for being patient with us."
Van Pelt made it easy for him by finishing with three consecutive bogeys, beginning with number 16. Van Pelt closed with an even-par 71.
"All in all, I'm proud of how I played. You have to give it to Tiger, he played well," said Van Pelt. "It was fun to be in that environment the last 36 holes."
Woods moved to the top of the PGA Tour money list and the FedEx Cup standings for the first time since 2009.
He sank a 22-foot putt for birdie at 15 to take the lead for a moment, but Van Pelt answered with a birdie of his own.
Both players struggled on the par-five 16th, where they each two-putted for bogey to drop to eight-under.
Woods parred 17 by hitting his third shot to six feet of the cup to grab the slim lead.
"I just controlled the pace and moved on about my business," Woods said.
Van Pelt said Woods is the top player on the PGA Tour right now.
"I think he's the only guy to win three tournaments on tour this year … on three different golf courses," Van Pelt said. "And he was leading the US Open after two days. So I'd say that he's playing the best golf in the world right now."
Australia's Adam Scott finished in third place at five-under-par 279. He matched the low round of the day with a four-under par 67.
Robert Garrigus (70), Jhonattan Vegas (71), Billy Hurley (72) and Noh Seung-yul (73) tied for fourth place at minus-four.
Third-round leader Brendon de Jonge, of Zimbabwe, stumbled to a six-over 77 and tied for 11th at one-under-par 283. – Sapa-AFP