Reeling from consecutive bogeys that dropped him out of the lead, Furyk recovered with birdies on four of his last five holes for a 4-under 66 and maintained his two-stroke lead over Woods at Firestone Country Club.
"It turned into a very, very good day," Furyk said.
It set him up for the biggest challenge of his career _ a chance to win a World Golf Championship by going head-to-head with the best player in the world playing his best golf of the summer.
Woods, in serious contention for the first time since he won the Memorial by seven strokes in late May, also had a 66. At stake today is a chance to become the first player to win three straight times at Firestone.
"Leading the golf tournament by two and teeing off with Tiger in the last group ... there's a lot worse positions I could be in," said Furyk, who was at 197. "I think most players would be excited to be put in that position and getting to test themselves."
Mickelson would have liked to have been part of the mix.
Instead, he teed off on No. 16 with a new ball that wasn't marked and sprayed it into the rough. He lifted the ball to make sure it was his _ but didn't tell his playing partner, Furyk, what he was doing.
That's a one-stroke penalty. A bogey turned into a double bogey and forced Mickelson to sign for a 70, leaving him six strokes behind.
Woods recovered from a rugged stretch early in his round for a 4-under 66, his seventh straight round at 67 or better at Firestone. While pleased with his position, Woods was even more satisfied with how he is playing.
"I feel a lot better about my game," Woods said. "I got myself right there, in contention with a chance to win."
Paul Azinger, taken over 11 other players as a Ryder Cup captain's pick, had a 65 and finished at 202, along with Darren Clarke.
Another stroke back was Ernie Els (66) and Colin Montgomerie, who is still trying to win an official event for the first time on American soil. He had a 66 and will be paired with Els, the South African who beat him in two U.S. Opens.
Bernhard Langer is probably too far back after a 68 put him at 204, but a strong showing will almost certainly secure a spot for him on the European Ryder Cup team.
Furyk made the team by finishing second two weeks ago at the Buick Open, and his strong play has continued. He tied for seventh in the PGA Championship, and has had at least a share of the lead after every round in the NEC Invitational.
His other victory this year was the Mercedes against a winners-only field. This one consists of 39 players from the Ryder Cup and Presidents Cup teams, and the top 12 Europeans from their Ryder Cup standings.
"It's a very elite field and a very strong field," Furyk said. "It would be a nice tournament to win."
Furyk missed the green on the fourth and fifth holes and failed to save par, dropping him two strokes behind Woods. But he made a nice par save after a bad drive on No. 6, then really got it rolling.
The final round appeared to be headed for a Woods-Mickelson showdown, a delicious prospect considering that Mickelson proclaimed Friday night that no one has played better than him throughout the year.
It changed quickly, thanks to great putting by Furyk and Mickelson's bad fortune.
While Mickelson chopped the 625-yard 16th, Furyk hit a wedge to four feet for birdie, then made birdies on the final two holes from about six feet.
Woods didn't have anything bizarre happen to him Saturday, a rarity considering what he has gone through this week _ food poisoning, left-handed shots and a few off tree roots.
He was solid with his irons and putted well throughout the way. With birdies from inside eight feet on the first two holes he claimed the lead and never gave it back until Furyk blew past him at the end.
At least Woods has a chance, something he hasn't had all summer.