Furyk, the 2003 U.S. Open champion, managed an even-par 70 on Saturday.
Woods, the reigning Masters and British Open champion, was a little inconsistent on Saturday. He flew out of the gate with birdies at three and four, but gave those strokes back before he made the turn. Woods bogeyed seven and nine to head to the back nine at even-par 35.
Woods got back on track with back-to-back birdies at 12 and 13, but fell to 9 under par with a bogey at the par-4 15th. Woods birdied the par-5 closing hole for the second time this week to take the lead as he tries to defend his title.
Furyk birdied the first, then parred his next six holes. He finished his front nine with a bogey at eight, but atoned for the miscue with a birdie at the ninth.
He limped into the clubhouse a bit with bogeys at the 12th and 17th holes, but a birdie at the last put Furyk within one shot of his Presidents Cup partner from this year's event.
Wen-Chong Liang carded a 2-under 68 and is alone in fifth place at minus-5.
Tetsuji Hiratsuka struggled to a 2-over 72 on Saturday, but has sole possession of sixth place at 3-under-par 207.
U.S. Open winner Michael Campbell shot an even-par 70 and is tied for seventh place with Nozomi Kawahara, who posted a 4-under 66 on Saturday, at two- under-par 208.
European Tour Order of Merit winner Colin Montgomerie played poorly in Saturday's third round. He carded a 7-over-par 77 and is part of a group tied for 48th place at plus-7.