Woods, a two-time winner of this event, stands at 8-under-par 136 after two rounds. First-round leader Henrik Stenson was four clear of Woods during round two, but struggled late en route to a 71. He is one back at minus-7.
Stenson flew out of the gate with a 4-foot birdie putt on one and a two-putt birdie on two to move to minus-8. Woods parred the first two holes and was four back at 4 under.
Woods cut that deficit by one with a 5-foot birdie putt on the third at Sherwood Country Club. Stenson pushed his lead back to four thanks to a 20-foot birdie putt at eight.
The first big swing of the round came at the ninth. Woods poured in a long birdie putt to move to 6 under, while Stenson stumbled to a bogey dropping his lead to two shots.
Woods moved within one as he drained another long birdie putt at the 10th. Stenson responded with a 12-foot eagle putt on No. 11, but gave those strokes right back as he faltered to a double-bogey at 12.
Woods got up and down for birdie from a greenside bunker at the par-5 13th to move to minus-8, where he joined Stenson in the lead. The one-putt was the sixth straight for Woods.
Stenson could not save par from a bunker on 14, but responded by sinking a 7-foot birdie putt on 15 to regain a share of the lead.
However, Stenson hit his second shot left of the green at the par-5 16th before pitching his third into a greenside bunker. After blasting out of the sand, Stenson two-putted for bogey to dip one back of Woods.
Woods closed with five straight two-putt pars, all of which came from within 30 feet.
'My iron game wasn't very good. I'm still struggling with my speed on the greens,' admitted Woods, who claimed two major titles among his eight wins in 2006. 'I kept blowing them by the hole today. Luckily a couple of them had train wrecks and went in. Otherwise, it was a little bit of a struggle today.'
Woods normally takes advantage of the par-5s, but struggled on them Friday. He only made one birdie on the long holes and saved par on the fifth by chipping in.
'I was 1-for-5 on the par-5s today, so that was not very good,' said Woods, who was the only player in the field to card a bogey-free round on Friday. 'I still have the lead. There is a long way to go, so hopefully I can put it together a little bit (Saturday).'
Ogilvy is tied for third after a 2-under 70 Friday. His round included five birdies and three bogeys.
'If I putted better today, I think I would have had a better score,' Ogilvy admitted. 'I felt like on the back nine especially, I made a crazy putt on 10 that was going pretty fast, but I missed three or four putts that were pretty makeable.'
Jose Maria Olazabal (70) and John Daly (71), both two-time major champions, share sixth place at 4-under-par 140. Padraig Harrington, David Toms and Colin Montgomerie are two strokes further back at minus-2.