Nelson carded a 3-under 69 Sunday, but squandered an opportunity on the 54th hole. Fuzzy Zoeller took third place at 15-under par after a final-round 70.
Quigley, who shared the second-round lead with Nelson and Zoeller, collected three birdies and a bogey through 13 holes to remain near the top of the leaderboard.
He birdied the par-5 14th to reach 16-under par and take the lead. Quigley missed the green long and left at the 15th and appeared to be in jeopardy of losing his place on top. Instead, Quigley pitched his ball 10 feet past the hole and converted the par save to remain in first place.
Quigley used sharp iron play all week to get to the top of the leaderboard and continued his fine form at the 16th. He knocked his short iron to four feet to get to 17-under, but Nelson was closing in on Quigley's lead.
Nelson, in the group behind Quigley, drained a 20-foot birdie putt at the 16th to get within one of the lead and added a 30-footer for birdie at No. 17 to tie Quigley for first at 17-under par.
Quigley, who knew Nelson made birdie thanks to the loud ovation he heard from the 18th fairway, once again let crisp iron play do his talking. Quigley stiffed his second two feet from the hole to set up birdie and take a one-shot lead with Nelson in the fairway.
Nelson had only a sand wedge in his hand when he attacked the flag on the left side of the green. He pulled it too far left and watched his ball bounce into a bunker. Nelson's blast out of the sand trap missed the hole and he two-putted for bogey, giving Quigley wins in four consecutive years.
'I was really, really psyched to come here for two months. I have been looking forward to getting started,' said Quigley, who pocketed $250,000 for the win. 'After six years I still don't think I belong in this company, but you add up the score after 18 holes and when you've got a low score it doesn't matter what name it is, you're going to beat them.'
Quigley teed it up in his 202nd consecutive event for which he was eligible and this one might indicate the possibility of a huge year.
'I really feel like I'm better this year than I've ever been,' said Quigley, who finished sixth on the Champions Tour money list in 2002. 'I keep getting better and I think that's the thing I'm the most proud of -- the fact that I'm improving.'
For Nelson, the winless streak continues. His last victory came at the SBC Championship in October of 2001, a season that saw him visit the winner's circle five times.
'I shot at it and missed,' said Nelson, referring to his errant approach at 18. 'It was disappointing after birdieing 16 and 17. Having an opportunity to birdie 18 would have been a lot of fun.'
Tom Watson shot a 5-under 67 on Sunday to finish in a tie for fourth place. He and Stewart Ginn completed 54 holes at 13-under-par 203, one shot better than Steven Veriato, who finished alone in sixth.
Tom Jenkins (69), Allen Doyle (69), Bruce Fleisher (72) and Bruce Lietzke (72) shared seventh place at minus-11.
Jack Nicklaus matched the low round of the day with a 6-under-par 66. He tied for 11th at 10-under par with 2002 winner Tom Kite, Ed Dougherty and John Jacobs.