Woods, the third-round leader, only managed a 2-over-par 72 on Sunday, while Yokoo posted a 1-under 69. The pair finished regulation tied at 8-under-par 272.
The reigning Masters and British Open champion played poorly on Sunday although his final round got off to a great start with a birdie at the first. He dropped a shot at the second, then double bogeyed the third to let several people back into the tournament.
Woods also bogeyed the eighth and 12th holes to move to 4 over par for the round. He birdied Nos. 13 and 15 to get to 8 under par, but had to wait to see if Yokoo could make a run at him.
Yokoo flew out of the gate with three birdies in his first six holes. He went into a serious funk after that with bogeys at nine, 11, 12 and 13 and it appeared Woods would successfully defend his title.
Yokoo rebounded with a birdie at 14, but dropped the shot with a bogey at 15. He was two down with three to play, but collected birdies at 16 and 18 to force the extra session with the top player in the world.
Jim Furyk, the 2003 U.S. Open champion, trailed his Presidents Cup partner by a stroke heading into the final round, but struggled on Sunday. He carded a 3-over 73 and took third at minus-6.
Katsumasa Miyamoto fired a 4-under 66 and took fourth at 5-under-par 275, followed by Gonzalo Fernandez-Castano, who also posted a 66 on Sunday. Fernandez-Castano came in fifth at minus-4.
Wen-Chong Liang shot a 2-over 72 and came in sixth at 3-under-par 277.
David Duval, who has not recorded a victory since this event in 2001, played poorly on Sunday. He managed a 5-over 75 and tied for seventh place with Hideto Tanihara, who carded a 1-under 69 in the final round. The pair finished at minus-2.
Reigning U.S. Open champion Michael Campbell also fell down the leaderboard on Sunday. He fashioned a round of 3-over 73 and tied for 13th place at plus-1.
European Tour Order of Merit champion Colin Montgomerie never got on track this week. On Sunday, the eight-time money leader in Europe made it around in 73 to tie for 46th place at 10-over-par 290.