Quigley, already in the clubhouse, was at 5 under par when Fleisher came to the 18th. Fleisher found the fairway off the tee but knocked his second into rough next to a front bunker. He chipped to four feet and calmly sank the putt to visit the winner's circle.
The win was Fleisher's first this season and his 17th since joining the Champions Tour in 1999. His first victory on the elder circuit came at this event that same year and Fleisher also hoisted the trophy in 2000.
'It's over. Thank God,' said Fleisher, who pocketed $217,500 for the victory. 'It's fun to win. The fans were great, my family was out here. It's a delight and I'm very, very thrilled.'
Quigley, six groups ahead of Fleisher, fired a 4-under 68 on Sunday to finish alone in second place at minus-5.
John Bland needed to eagle the par-5 closing hole to match Fleisher at 6 under but instead made par. He shot a 1-over 73 and tied Gil Morgan for third place at 4-under-par 212. Morgan posted a 2-under 70 in the final round.
Wind was a huge factor in the final round as conditions were very difficult. Only two players broke 70 on Sunday but the tournament came down to three players.
Quigley was in the clubhouse at minus-5, while Fleisher and Bland were completing the back nine. Fleisher was steady, starting at the par-5 14th when he found a bunker with his second shot. He blasted out to the collar of the green and two-putted for par.
At the 15th, Fleisher drove into a fairway bunker and was forced to lay up short of the green. He pitched to 20 feet and canned the par-saving putt to keep his share of first place.
Fleisher picked up a brilliant sand save at the 16th, then drained a four-footer for par at the par-3 17th.
After Fleisher scrambled for his birdie at 18, the tournament was up to Bland, who joined Fleisher and Quigley at 5 under, thanks to a birdie at the 14th. Bland missed a seven-footer for par at the 17th to fall to minus-4 and trail Fleisher by two.
At the 18th, Bland drove into the first cut on the left side. He tried to reach the green in two but instead found the grandstand left of the putting surface. Bland took his drop and needed to hole the pitch but ended up left of the green.
'I was very fortunate today,' admitted Fleisher, who resides in nearby Ballen Isles, Fla. 'It was very difficult. The scores show it. Dana must have played out of his gourd. He always does.'
This is Quigley's second consecutive runner-up finish on the Champions Tour. He finished second to Fuzzy Zoeller at the season-opening MasterCard Championship.
Quigley began the round in a tie for 20th place and nearly pulled off the amazing comeback.
'You never leave winning out of your game plan,' said Quigley. 'Anything can happen on a golf course this hard. I was basically doing what everyone else did out here - trying to survive.'
Jim Thorpe matched Quigley for low round of the day honors with a 4-under 68. He shared fifth place with Mark McCumber (70), John Jacobs (72) and overnight co-leader Wayne Levi, who struggled on the back nine Sunday and finished with a 75. The group came in at 3-under-par 213.
Tom Jenkins (72), Tom Kite (73), Ed Fiori (74) and Morris Hatalsky (74) tied for ninth place at minus-2.
Don Pooley, who shared the lead with Levi after the second round, carded a 5-over 77 and tied for 13th at minus-1.