Woods, currently the No. 1 player in the world rankings and the reigning Masters and British Open champion, shot a 3-under 67. Duval, the overnight leader who has struggled since his 2001 British Open breakthrough, posted a 2-under 68 and joined Woods at minus-8.
Duval, who has battled back injuries that have seen him make only one cut this season on the PGA Tour, got out to the first-round lead with a 64 of his own on Thursday.
On Friday, Duval got off to a shaky start with a bogey at the first hole. He parred out the rest of his front nine, but dropped another shot at the par-4 10th.
That would be Duval's last mistake. The former No. 1 player in the world collected back-to-back birdies at 11 and 12, then added another at the 16th. Duval, who won this title in 2001, birdied the closing hole to get within one shot of Furyk's lead.
Woods, whose win here last year was his first since the WGC-Match Play Championship in February, bogeyed the second, but atoned for the mistake with two birdies in a row from the fourth. He dropped another shot at six, but moved up the leaderboard with solid play from there.
He birdied the ninth, then recorded birdies at 13 and 15 to join his good friend Duval in second place.
Tetsuji Hiratsuka and Kaname Yokoo both shot rounds of 3-under 67 on Friday and are tied for fourth place at minus-5.
Wen-Chong Liang (65), S.K. Ho (67) and Tomohiro Kondo (70) are knotted in sixth place at 3-under-par 137.
Reigning U.S. Open champion Michael Campbell carded a 4-under 66 and is tied for ninth place with Prayad Marksaeng (69), Gonzalo Fernandez-Castano (66), Toru Suzuki (67) and Tsuyoshi Yoneyama (66). The group is knotted at 2-under-par 138.
European Tour Order of Merit winner Colin Montgomerie shot a 1-under 69 and is part of a group tied for 20th place at even-par 140.