Yokoo, a regular on the PGA Tour, fired a bogey-free 65 to reach 11-under-par 131 and grab a four-shot lead over Spain's Sergio Garcia (68), England's Justin Rose (69) and Myanmar's Zaw Moe (67).
'I made some great putts today,' said Yokoo. 'I'll just try to keep playing like this on the weekend.'
Woods holed a 40-foot chip for eagle at the par-5 fourth hole but did not do much else in the second round at Phoenix Country Club. He missed an eight-foot birdie putt at the ninth and could not manage another birdie until the 16th hole.
Woods, who is making his third appearance in Japan, knocked a sand wedge to six feet to set up birdie at No. 16 to polish off his round of 68.
'I hit the ball a lot better today,' said Woods, who began the second round seven strokes behind first-round leader Darren Clarke. 'The good thing is I'm playing better and hopefully I can play like this on the weekend.
'I hit some good putts, but misread a couple and that added up to a lot of missed chances. If I hit the ball like I did today and make the putts I'll be in good shape. But a lot of it depends on what Kaname does because he's playing very well.'
Garcia birdied four of his last six holes to move up the leaderboard.
'If I play like I did at the end of today's round I like my chances,' Garcia said. 'I played pretty poorly on a few holes but am still in good shape.'
David Duval, the defending champion, posted his second 2-under-par 69 in as many days and is seven strokes behind Yokoo.
Clarke collected five birdies and six bogeys for a 1-over-par 72. He stands at 6-under-par 136.
Scores from the Dunlop Phoenix Open