Jason Gore shot a 5-under-par 65 and is alone in second place at the South Course at Firestone Country Club. Lucas Glover, snubbed by United States Ryder Cup captain Tom Lehman for one of his picks, carded a 4-under-par 66 and is third.
'You can get fired up in a heartbeat,' said Woods, who has won his last three starts dating back to the British Open. 'This is a World Golf Championships event and on top of that, this is one my favorite golf courses in the world.'
Woods had an up and down front side at Firestone. He carded three birdies and two bogeys on the opening side, then rattled off six consecutive pars to begin his back nine.
At the par-5 16th, even Woods could not reach the green in two. He spun a wedge back to 5 feet from 76 yards out and converted the putt. Woods hit an average pitching-wedge at the closing hole that stopped 20 feet from the flagstick.
He rolled in the birdie try to grab his share of fourth place.
'I didn't hit the ball very good starting out, but I fixed a couple of things on the back nine,' admitted Woods. 'I really played a pretty good back nine, then got myself four back of the lead.'
Davis Love III, Michael Campbell, David Howell, David Toms and Luke Donald, who shared third place with Scott and Sergio Garcia at Medinah, joined Woods at 3-under-par 67.
Scott began on the back nine Thursday and did not get off to the kind of start one thinks of for a leader. He drove into the right rough, chipped out, wedged on, then three-putted for a bogey. The young Australian parred his next five holes before his ascent up the leaderboard.
At the long, par-5 16th, Scott laid up with a 6-iron, then hit a lob-wedge to 5 feet. He rolled in the birdie putt and added a 7-footer for birdie at 18 to make the turn at 1 under par.
Scott caught fire at the start of his second nine. At one, Scott knocked a sand-wedge to a foot and tapped-in for birdie. He two-putted for birdie at the par-5 second and made it four in a row with another kick-in birdie at the third.
'I drove the ball really well today, pretty long and straight, and had a lot of wedges,' said Scott. 'I hit a lot of shots 5 feet and in and took a lot of pressure off my putting.'
Scott was not done moving up the leaderboard, but first came another hiccup. At the fourth, Scott hit a 6-iron for his second, but three-putted for another bogey.
He stood at 3 under par for the championship, but had another torrid run of birdies in him. Scott hit a 7-iron to 4 feet to set up birdie at the fifth, then made it two in a row when his 8-iron second at the sixth stopped 2 feet from the stick.
Scott parred the seventh, but came right back at No. 8. He hit driver off the tee, then hit a lob-wedge to 20 feet. Scott ran that birdie putt home and closed with a tap-in birdie at nine to grab the lead and post a second-nine 29.
Scott, whose best finish in this event has been a tie for 36th last year, saw this strong round coming after last week's PGA Championship, where he went 69-69-67 to tie for third place.
'I played really well last weekend at Medinah,' acknowledged Scott. 'It was just something to keep the good vibes going from there and carry over here. I knew I was swinging well enough and just waited and the good shots came and rolled in a couple of nice putts.'
Ernie Els, Olin Browne, Kevin Stadler, Chris DiMarco, Tim Clark, Jose Maria Olazabal and Chad Campbell are knotted in 10th place at 2-under-par 68.
Reigning Masters champion Phil Mickelson struggled Thursday with a 4-over-par 74 and is tied for 56th place.