Phil Mickelson sank a 15-foot birdie putt on the last hole to shoot a third-round 69 and climb to minus-10 alongside Steven Alker. Briny Baird, Fred Couples, Jonathan Kaye, Arron Oberholser and Carl Pettersson are one stroke farther back at 9-under-par 207.
Woods, who has won 26 of the 28 times he has led entering the final round on the PGA Tour, will be paired with Faxon and Mickelson in the final group on Sunday. Mickelson is the last player to defeat Woods when he was leading after three rounds, which happened at the 2000 Tour Championship.
The final pairing will be interesting as Woods and Mickelson are trying to put controversy behind them. Mickelson referred to Woods' equipment as 'inferior' in a recent interview but the duo has reportedly settled any differences they may have had.
'I'm looking forward to tomorrow,' said Woods, the 1999 Buick Invitational winner. 'After taking as much time as I took off. I'm excited about getting out there and competing and we have got a great final group. So it's going to be a lot of fun.'
'I was thinking on that putt on 18 I would love to get into that last group,' said Mickelson. 'I love the challenge of it. And Tiger's probably not even a hundred percent, he hasn't played competitively for some time. He's had surgery and he's been rehabbing that. And yet he's still atop the leaderboard, still leading the tournament. So it shows you what a great player he is. And I love the opportunity to play with him and compete against him.'
Woods, playing in his first tournament since December knee surgery, got off to a quick start with consecutive birdies starting at the first. He followed that up with a birdie at the par-5 sixth.
'I got off to a great start,' Woods said. 'Birdied the first two and just kind of grinded my way along today. I didn't hit the ball particularly well, but I got up-and-down from a lot of places today.'
The No. 1 player in the world however faltered at the next and went on to make the turn at 10-under.
The eight-time major winner continued his dominance of the par-5s on the back nine. He birdied both, Nos. 13 and 18, to climb into the lead.
Woods scrambled for his birdie on 18. He drove his ball down the right side of the fairway, but then found trouble. His second shot sailed into the bleachers right of the green. After a free drop, he nearly holed out for eagle before rolling in a short birdie putt to take the lead.
'Well I feel a lot better today. I have felt a lot more comfortable with my driving today,' said Woods. 'I hit some better shots off tees. It's just one of those things where I just need to go out there and hit a few balls after I'm done with this and just kind of get back in that rhythm again.'
Faxon had an inconsistent round of 71. He started with back-to-back birdies starting at No. 2. He dropped a shot with a bogey at the par-4 fourth, but responded with a 12-foot birdie putt at the next to get back to 12-under.
Faxon, a seven-time winner on the PGA Tour, later bogeyed the seventh before birdieing the ninth to make the turn at minus-12.
'I didn't make any many pars early on,' said Faxon. 'The golf course is really new for me. I didn't play last year and my first round was actually the round that was broken up over two days. But you got a real golf course here. There's a lot of good spots to put the pins and you can get them in some corners where it's really hard to attack.'
Around the turn, he made another birdie at the 10th to briefly claim a two-shot lead at minus-13. He then bogeyed two of his next three holes, both of which were due to three putts, to drop back into second place.
The 2001 Sony Open winner is looking forward playing with Woods and Mickelson.
'I don't think I have played in the last group with World's 1 and 2,' said Faxon, who didn't realize Mickelson has fallen to No.3 behind Ernie Els. 'I'm going to kind of get lost in the shuffle a little bit. I think Phil's going to have a little bit more of a home crowd. Tiger, everybody wants to see him play, because he hasn't played at all this year. So it's going to be mayhem out there. But I'm looking forward to it. I've played with both the guys, but I never played with both of them together.'
Mickelson shot his second 69 of the tournament despite a double bogey. 'Lefty' carded three straight birdies starting at No. 2 to climb to 10-under. He then parred the final five holes on the front side and the first two on the back.
'I played well today and the course was playing very difficult,' Mickelson said. 'But I did get off to a really good start and had a chance to go really low. But I let a few things slide midway through the round. I missed a couple of short birdies on six and nine.'
Mickelson went on to double bogey the par-4 12th, his second double bogey of the tournament. He responded with a birdie at the next to reclaim one of those strokes. Mickelson, who owns 21 PGA Tour wins, birdied the 18th to get back to 10-under and set up a final-round duel with Woods and Faxon.
'I felt like because I drove it well it was an easy 69,' said Mickelson. 'Because I hit more fairways today than I did the first two days combined. And that gave me a chance to go at a lot of pins, especially with the lift-clean-and-place.'
Charles Howell III, Mark Calcavecchia, Marco Dawson, Luke Donald, Spike McRoy, Craig Perks, Rory Sabbatini and Bob Tway are tied for 14th at 6-under 210.
Darren Clarke, who was tied for 22nd at 5-under 211, was disqualified for signing an incorrect scorecard. Clarke signed for a par-4 on the 12th, but actually scored a bogey-5 on the hole.