Tiger Woods, the 2002 champion, posted a 6-under 66 and is in the hunt for his first stroke-play title since the World Golf Championships - American Express Championship last year.
He is at 15-under-par 201 and is tied with last week's U.S. Bank Championship in Milwaukee winner Carlos Franco, who bogeyed the 18th at Warwick Hills Golf and Country Club to shoot a 67.
'You can't afford to make any bogeys,' said Woods, who has tallied only one through three rounds. 'To have one is pretty good. I'm starting to play a little better now.'
Singh has tried to supplant Woods atop the world rankings and last year topped Woods on the PGA Tour money list. However, on Sunday, it will be Woods chasing Singh.
Singh shared the 36-hole lead with defending champion Jim Furyk and Billy Andrade, but broke out of the pack with back-to-back birdies at two and three. Singh two-putted for birdie at the seventh, then sank a 20-footer for birdie at eight to go to 15 under par.
But Daly hung tough. Daly hit a spectacular punch shot from the trees at the ninth. His ball stopped 15 feet from the hole and he drained the birdie putt to get to minus-14. Daly, who won this year's Buick Invitational, rolled home an 8-foot birdie putt at the 10th to draw even with Singh.
Singh pulled ahead with a 4-foot birdie putt at 10. He added another at the par-5 13th although he looked to be in trouble when his second landed in the back bunker. Singh blasted his long, downhill bunker shot 8 feet past the hole, but ran home the birdie putt to go to 17 under and two clear of Daly.
Daly did well enough to stay in the hunt. At the driveable par-4 14th, Daly landed in a bunker in the fifth fairway. Faced with trees in front of him, Daly chipped to the rough, then pitched to 3 feet. Daly tapped in the par save, then holed a tough 8-footer for par at the next after his approach nicked a tree.
Singh was up two, but Woods and Franco charged up the leaderboard. Woods drained a 30-footer for birdie at 13 and made it two in a row at the 14th. The No. 1 player in the world drove into the right rough then hit a huge hook into the left trees. Woods hit a low chip 5 feet from the stick and converted the birdie try.
Franco flew up the board with four birdies in a row from the 11th, but made a mess of the par-5 16th. He was forced to lay up short of the putting surface, then sailed over the green with his third. Franco chipped on, but two-putted for a bogey.
Singh, playing with Franco, two-putted from 55 feet for birdie at the 16th, but Daly got within two while Singh was on 16. Daly knocked his approach inside 4 feet at the last and made the birdie putt to stay within two.
Singh had an easy chance to extend the lead at the last. His second stopped inside of where Daly hit his, but Singh badly pulled his birdie putt. Singh settled for par and the 54-hole lead, which has been a good landmark for the 1997 champion.
The last six times Singh has held the 54-hole lead, he has gone on to visit the winner's circle.
'I played nicely,' said Singh, a three-time winner this season. 'I'm very happy with my golf swing. I'm happy with my performance now and I'm really happy with putter.'
Singh returned to a conventional putter after more than two years with the belly putter. He needed 27 putts on Saturday and has averaged slightly over 28 putts for the week.
'I played like this the first two days as well, but made a few more putts today and the first day,' said Singh, who took 26 swipes with the flat stick en route to a 63 on Thursday. 'I feel like I got some touch back.'
Daly shot a 6-under 66 on Saturday.
With three tournaments remaining before the American Ryder Cup team is finalized, Daly is not in the top-25, but if he can overcome Singh on Sunday, he will be in the mix and potentially a pick for captain Hal Sutton.
'Whatever Hal does, I'm for him,' said Daly, who has never played in a Ryder Cup, despite winning two majors. 'If I get in, I get in. At least I'm trying and that's all you can do.'
Daniel Chopra carded a 6-under 66 and is alone in fifth place at 14-under-par 202.
Furyk managed a 2-under 70 and is knotted in sixth with Olin Browne, who shot a 69 on Saturday. The duo is tied at 13-under-par 203.
Matt Gogel (68) and Stewart Cink (70) are tied for eighth at minus-12, while Jeff Sluman has sole possession of 10th place after a third-round 68. Sluman is at 11-under-par 205.
Andrade struggled to a 1-over 73 and is part of a group in 11th at minus-10.