Zach Johnson climbed into second place at 17-under-par 199 thanks to a third- round, 7-under 65. He is two strokes clear of Masters runner-up Chris DiMarco, who posted a 6-under 66 on Saturday to get to minus-15.
Singh, the reigning PGA Champion, came flying out of the gate with birdies on one and two, both from within 10 feet before he made it three straight as he birdied the third on Warwick Hills Golf and Country Club to move to 16 under, six clear of Woods.
The Fijian sank a 14-foot birdie try on the fifth and then birdied six as well. Despite his hot play, Singh only led Johnson by four strokes. Singh missed a short birdie try on seven, but then birdie eight to move to minus-19.
Singh sank a 13-foot birdie try on nine to move five clear of Johnson.
'You can't always play two nine holes of golf like I did the front nine,' Singh said. 'Otherwise, you'd be shooting 56s and 57s.'
Singh cooled down with back-to-back pars from the 10th. He drove within 30 yards of the green at 12 and got up and down for his birdie from there.
The world's second-ranked player two-putted for birdie at 13. After a pair of pars, Singh missed a short par putt on 16 to slip back to minus-21, but got that shot back with a 7-foot birdie putt on the 18th to lead by five entering the final round.
'It was incredible. The putter started working. It woke up finally,' said Singh, who has struggled with the putter this year. 'You know, I was very confident out there. I was very focused on what I was doing. I just went out there and played golf, and that's what I told myself today, go out and hit the shots and try to roll some putts in. They started going in.'
Singh has led 23 times after three rounds and gone on to win 15 of those tournaments. Singh, who won this crown in 1997, as well as last year, could become the first player to win this title three times and just the second back-to-back winner here.
'I don't know, it would be great if I could win it, but I've still got a hard 18 holes of golf to go,' said Singh, who could join Tony Lema as the only back-to-back winners here with a victory. 'It's a golf course where I have to go out there and make birdies as well. I cannot go out there and sit back and wait for the guys to catch me. I have to increase my lead if I can.'
Woods bogeyed three straight holes from the second to tumble to minus-9, seven shots back of Singh, who he played with on Saturday. He got one of those shots back with an up-and-down birdie on seven.
The world's No. 1 player then ran in a 30-footer for birdie on nine and parred 10 and 11 before catching fire.
He drove into a greenside bunker at the 12th and got up and down for birdie. Woods' most remarkable birdie came on the 13th. He tried to play a hard hook from the left rough with his second shot, but the ball carried long, right of the green into the water.
Woods took the lateral drop, which happened to be on the green and drained a bending 60-foot birdie putt to get to 13 under.
The 29-year-old then two-putted for birdie on the short 14th after driving the green. Woods two-putted for birdie on 16. He lost his drive well right at the last. Woods hit a stellar shot over several trees into a greenside bunker. However, he was unable to save par to finish at minus-14.
'The hardest thing in golf is to follow up a great round,' said Woods of his second-round 61. 'I had a hard time today unfortunately. I got off to just a terrible start, but put it back together though. I got it back in the round, and I was 3 under par, but the last hole summed up the whole day.'
Johnson opened with a birdie on the first and posted three birdies in a four-hole stretch from the fourth.
Around the turn. the 2004 BellSouth Classic champion birdie No. 10 to move to minus-15. Johnson birdied the 12th, then sank consecutive birdies from the 14th to get it to 18 under. He faltered to a bogey on the par-5 17th, though, before parring the last.
'You can't get caught up in what others are doing,' said Johnson of how Singh was playing. 'I think first and foremost, when you're hitting it well and putting it well, you can put up good numbers. So you have to stay within yourself. It's a matter of momentum out here and I fortunately got it early.'
Olin Browne fired an 8-under 64 to move to 13-under-par 203. He was joined in a tie for seventh by Jason Bohn (69) and Steve Lowery (68).
Briny Baird, Craig Barlow, Jeff Brehaut, Fred Funk, Larry Mize and 2003 champion Jim Furyk are one stroke further back at minus-12.