Sergio Garcia, Jonathan Byrd, Jerry Kelly, Daniel Chopra and overnight co-leader Peter Lonard shared third place at 6-under-par 134.
Woods has been wrestling with his shots off the tee and the erratic driving that saw him blow the 36-hole lead at the Wachovia Championship last week has followed him to Texas. The difference, however, is that the top player in the game is sinking every putt in sight.
'I've putted well all year except for one week,' said Woods. 'Augusta is the only week I putted poorly. I didn't have any three-putts there, which is good, but I didn't make any putts, either. So consequently I wasn't in contention there.'
Woods improved his driving somewhat from his opening-round 65 which he posted at the TPC at Four Seasons, but Cottonwood Valley, the other course in rotation for the first two rounds, provided a different test.
'I've never played Cottonwood that way but I've played TPC that way,' said Woods. 'It was interesting trying to get your lines and your bearings off the tees because I've never seen the wind come from that direction before.'
He hit his tee shot to 20 feet for a birdie at the par-3 second but struggled to a bogey at the very next hole.
Woods took advantage of the other par-3 on the front nine, the ninth, and left a 7-iron within a foot of the hole. He tapped in for birdie and drained a 12-footer for a birdie at the par-3 12th to move to 7 under.
At the par-5 16th, Woods scrambled toward the green after his drive found the rough. He managed to knock his third within a few feet of the hole for birdie and the outright lead.
'I would have taken anything under par today,' said Woods. 'Even par or under par would have been a good score. With the wind blowing as hard as it was and as cool as it was, the ball just was not flying.'
O'Meara, who has had a solid campaign in 2004 that includes a victory at the Dubai Desert Classic on the European Tour, picked up a birdie at the fourth and added a birdie at the 10th to continue his climb up the leaderboard.
The 47-year-old added birdies at the 13th and the 16th to join Woods in the last group on Saturday after a bogey-free round of 66.
'We've played in major championships together on Sunday or Saturday at the British Open a couple of times, and we've played together before,' said O'Meara, who won the Masters and British Open in 1998. 'He's usually in the last few groups on the weekend.'
Garcia used another strong finish to remain in contention. On Thursday he collected five birdies over the last six holes at Cottonwood Valley and made another late push Friday at the TPC.
After a birdie and a bogey on the front nine, Garcia three-putted for a bogey at the 13th before catching fire down the stretch.
The Spaniard dropped his approach inside 7 feet for a birdie at the 15th and made it two in a row with a birdie at the very next hole. Garcia then left himself within 20 feet for a birdie at the last and drained the putt to complete a round of 68.
'Every time you're back in contention, no matter where, you're always happy,' said Garcia, who tied for fourth at the Masters. 'I'm definitely happy that I'm back there. I definitely feel like I should be a lot better than I am at the moment, but that's the way it is, and that's why this game is so tough.'
Defending champion Vijay Singh was lurking as always after the second round. Singh shot a 67 to share eighth place with reigning PGA champion Shaun Micheel and Stephen Leaney at 5-under-par 135.
J.L. Lewis, who shared the first-round lead with Lonard, managed a 4-over 74 to finish six shots off the pace in a group at 2-under-par 138.
The 36-hole cut fell at even-par 140 with 80 players qualifying for the weekend.
Masters champion Phil Mickelson ran off three bogeys over his first nine holes and never recovered. Mickelson, who had finished in the top-10 in 10 of his previous 11 tournaments this season, posted a 2-over 72 to finish at 1-over-par 141 for his first missed cut since the Chrysler Championship in November of last year.