Greg Owen moved into third place at 10-under-par 206 thanks to a third-round 70. Brett Quigley, who shared the second round lead with Coles, tripped to a 1-over 73 and shares fourth place with Jose Maria Olazabal at minus-9.
Singh, who matched the course record of 64 on Thursday, fell one shot behind Coles and Quigley after two rounds. The Fijian slipped further off the pace with bogeys fourth and sixth that dropped him to minus-7.
The 42-year-old fought back with a birdie at the eighth from 10 feet out. Singh drained a 12-foot birdie putt at the par-four 10th on Redstone Golf Club to get back to minus-9.
Singh, who collected his 25th career win earlier this year and was voted into the World Golf Hall of Fame earlier this week, got within one of the lead with a birdie at the par-5 12th. He then got up and down from short of the green at the par-5 15th for birdie to grab a share of the lead.
'I'm quite happy with my position right now, but the golf course is getting tougher every day,' said Singh. 'The first day it was nice and soft and got a little bit more difficult yesterday, and today it was a beast out there. I'm quite happy with the way I finished. I didn't play as good as I wanted to the first nine, but the back nine I got a few back.'
Coles -- who is one of the shortest hitters on tour, ranking 181st in driving distance -- moved out to an early two-shot lead as his birdied the par-5 first and Quigley bogeyed the same hole. Coles climbed to 12 under with a 20-foot birdie putt at the fifth.
The Australian, who owns two wins on the Nationwide Tour, stumbled back into a share of the lead with consecutive bogeys from the seventh. Coles righted the ship with a birdie on No. 9 to regain a one-shot lead. However, he parred his final nine holes to remain at minus-11.
'It got pretty windy and pretty tough and I didn't hit it as good as I did the first couple of days,' Coles said. 'I've got an opportunity to learn from tomorrow's round. I'm going to learn from it and I'm going to be better. Whether I win or I don't, it's all about learning to cope with the emotions and the pressure of being in that situation.'
Owen grabbed a share of the lead after birdies at the second and seventh. After four consecutive pars around the turn, he rejoined Coles atop the leaderboard with a birdie at the 12th.
The 33-year-old Owen took a one-stroke lead with a birdie on the 16th. However, the Englishman faltered to back-to-back bogies from the 17th to end one shot behind the leaders.
Tom Byrum moved into a tie for sixth place with a 2-under 70. He was joined at 8-under-par 208 by John Daly and Joe Ogilvie, who each carded 1-over 73s in round three.
Jeff Maggert had moved into a tie for the lead with a birdie at the ninth, but he played his final nine holes at plus-3. He ended at minus-7 and was tied there by Brian Bateman, Charles Howell III, Kent Jones and Stephen Leaney.