Phil Mickelson, who earned his second major victory on Monday at the PGA Championship, bogeyed two of his last five holes in the second round, en route to a 2-over 72. He is tied for 20th place at plus-1.
Woods recorded his first birdie at the par-3 fifth when his 15-footer fell into the bottom of the cup. He added a 12-foot birdie putt at the 10th to reach 6 under par for the championship.
The No. 1 player in the world found trouble off the tee at the par-4 14th, and he was forced to lay up short of the green. Woods knocked his third to 20 feet, but missed the par putt to fall to minus-5.
Woods reclaimed the lost stroke at 15 after his 5-iron tee ball stopped 12 feet short of the hole. He stood at 6 under par again, but landed in the tall grass at 18.
His drive came to rest in the trees on the right and Woods attempted a low shot under a branch. His ball nailed the tree and kicked farther right. He got a drop because of a scoreboard obstruction, then knocked a 7-iron over the green with his third.
Woods' chip came up 25 feet short and he missed the bogey putt. He tapped in the putt for double bogey and fell back into a tie for the lead with Donald, who was in the clubhouse.
'It was an easy second shot and I had all the room in the world to put it up there,' said Woods, the reigning Masters and British Open winner. 'I hit it straight left and hit the tree. I thought I played well all day, just until the last hole.'
As for Donald, the Englishman began his second round on the back nine and found trouble early. He drove into the rough at the 11th and could not save par, but that would be the last miscue for the European Ryder Cupper.
He hit a 9-iron to 25 feet to set up birdie at the 13th, then played a 6-iron to 6-feet at the 14th to record back-to-back birdies. Donald polished off three birdies in a row at the par-3 15th when he knocked a 5-iron to six feet.
Donald parred his next four holes around the turn. At the par-5 second, he reached the fringe with his 3-wood second shot, then chipped to 5 feet where he drained the birdie putt.
With Woods' mistake at the 18th, and Donald's solid play on the remainder of his round, Donald finds himself tied for the lead.
Donald has one WGC title, he split the World Cup with fellow countryman Paul Casey last year, but the 16th-ranked player in the world might be ready for an individual win.
'I'm trying to treat this as a fun week, there's no cut so you're guaranteed to finish somewhere,' joked Donald. 'It's obviously a high-class field and I want to do well.
'I enjoy playing with Tiger. I think the kind of atmosphere and the energy he brings with him, with the crowd and stuff, I thrive on that. Hopefully, the weather will stay good.'
There are forecasts for thunderstorms Saturday afternoon so tournament officials pushed up tee times. The players are going in threesomes off both the first and 10th tees and the last group is slated to tee off at 9:20 a.m. (ET).
Justin Leonard, who was named as one of Jack Nicklaus' captain's picks for the American Presidents Cup team on Monday, posted a 4-under 66 on Friday. He is tied for eighth place at 2-under-par 138 with Stuart Appleby (70), David Howell (68) and David Toms (67) and Sergio Garcia (70).
Defending champion Stewart Cink will have a lot of ground to make up he is to repeat. He shot a 2-over 72 in the second round and is tied for 32nd at plus-4.