Defending champion Vijay Singh carded a 1-under 71 just a day after he matched the course record at Redstone Golf Club. Singh finished at 9-under-par 135 along with John Daly, Jeff Maggert and Joe Ogilvie.
The 35-year-old responded with a birdie at the very next hole and drained a 15-foot putt for a birdie at the par-4 17th. Quigley gave that shot back with a bogey at the 18th but he countered again with a birdie at the following hole.
Quigley then played a wedge to 8 feet for a birdie at the par-4 fourth and two-putted for a birdie at the par-5 ninth to join Coles in the lead.
'Yesterday I played flawless and today was pretty ugly but I managed it well,' said Quigley, who is trying to win for the first time on the PGA Tour. 'I putted well the last two days and I'm just happy. It sounds pretty easy, and certainly when I've got a good attitude, it is pretty easy.'
Coles also started on the back nine and found trouble early with a bogey at the 10th. He recovered with a birdie at the 11th and ran off back-to-back birdies from the 14th to reach 9 under.
The Australian chipped in for a birdie at the par-4 18th and jumped to 11 under with a birdie at the par-4 sixth. Coles found trouble with a bogey at the par-4 seventh, however, and parred his way in for his piece of the lead.
'It's only Friday,' said Coles, who is also going for his first PGA Tour title. 'There's two more days to go. I don't like to get ahead of myself too often.'
Daly collected four birdies on the front nine before stumbling to a bogey at the 10th. Daly came back with a birdie at the par-4 14th after his second shot stopped within 3 feet of the hole and he made it two in a row with a birdie at the par-5 15th.
The 38-year-old faltered with a bogey at the 17th and hit a bad drive at the closing hole. Daly had a look at the green, however, and played his second shot to two feet for a tap-in birdie and a round of 67.
'It's been nice to make a few putts, especially today,' said Daly. 'All in all, it just felt really good and it's nice to hit the ball solid. It just feels great to make some putts finally.'
Singh was in control early with a couple of birdies on the front nine but he hit his drive into the water at the par-5 ninth en route to a bogey. Singh then parred nine straight holes coming in to finish one shot back.
'I hung in there,' Singh said. 'It was one of those days that could have gone either way, and I just stayed very steady and played each hole at a time.'
Maggert started on the back side and picked up a quick birdie at the 10th. He then birdied the par-5 15th and added a birdie at the 17th.
At the par-4 18th, Maggert dropped his approach inside 10 feet and converted the putt to move to 9 under. He moved into the lead with a birdie at the second but struggled to a bogey at the seventh for a round of 68.
Ogilvie reached 10 under with a birdie at the 15th but he bogeyed the very next hole on his way to a round of 67.
Greg Owen shot a 69 to finish alone in seventh place at 8-under-par 136. Jose Maria Olazabal, Mark Calcavecchia, Thomas Levet, Bo Van Pelt and Carl Paulson share eighth place at 7-under-par 137.
A total of 78 players survived the 36-hole cut which fell at 1-under-par 143. Chad Campbell and former PGA champion Shaun Micheel posted matching rounds of 71 to miss the cut by a single stroke.