Former U.S. Open champion Jim Furyk, Tomohiro Kondo and Shinichi Yokota are tied for third place at 3-under-par 67 at Phoenix Country Club.
Duval, who won this title in 2001, opened on the back nine Thursday and collected two birdies in his first four holes. He closed with back-to-back birdies at 17 and 18 to make the turn at 4-under-par 31.
He birdied the par-5 fourth to get to 6-under par for the championship. Problems arose for the player who was ranked No. 1 in the world during 1998-99. Duval posted two bogeys in a row from the fifth to fall back to minus-5, but a birdie at the ninth gave him sole possession of the lead.
Woods, whose win here last year was his first since the WGC-Match Play Championship in February, also started on the back nine Thursday. He birdied the 10th, but parred his next five holes.
The reigning Masters and British Open champion birdied 16 and 18 to head to his second nine at minus-3. Woods began his back side birdie-bogey-birdie, but a birdie at the eighth got him within one of Duval.
Kaname Yokoo, Hidemichi Tanaka, Mamo Osanai, Mitsuhiro Tateyama and Tetsuji Hiratsuka are knotted in sixth place at 2-under-par 68.
Colin Montgomerie, who won his eighth Order of Merit title this year on the European Tour, is part of a group tied for 25th place at 1-over-par 71.
Current U.S. Open champion Michael Campbell is in 37th place after a 2-over- par 72 on Thursday. Thomas Bjorn, who visited the winner's circle here in 2003, struggled to a 6-over 76 in round one and shares 79th place.