'I didn't expect to be here doing this today,' said Watson, who pocketed $440,000 for his third victory at this event. 'It was a round that I'll always remember.'
'When a guy shoots 64 in front of you, it's pretty tough,' said Quigley, who did capture the Champions Tour money title. 'All in all, it was a great year. I played my heart out all year, so I have nothing to be ashamed of.'
Jay Haas, the overnight leader, blew a six-stroke advantage in his bid to win his third tournament in four starts. He shot a respectable, 1-under 71, but came in second at minus-15.
Tom Kite posted a 5-under 67 and came in third at minus-13. Defending champion Mark McNulty carded a 4-under 68 on Sunday and took fourth at 11-under-par 277.
Watson and Haas were tied at 15 under par when Watson reached the tee at the par-4 closing hole. He hammered his drive down the middle, but came up 25 feet short with his 7-iron approach. Watson sank the birdie try to go one ahead with Haas and Quigley in the fairway.
Haas hit a solid second shot 20 feet left of the hole, but missed the birdie putt, giving Watson his second win of the year to go along with the Senior British Open.
'I'm very grateful to have been able to make those critical putts at the right time,' said Watson. 'The greens tested your skill with the flat stick. I finally got used to in the last round.'
Watson wasted little time in cutting into Haas' lead. He rolled in a 15-foot birdie putt at the second, then mixed two birdies and a bogey over the next five holes.
At the par-5 eighth, Watson ran home a 25-footer for birdie, then he added another at nine after he drove into a fairway bunker. Watson drained a 12-foot par save at the 10th and suddenly found himself two back.
Haas birdied the same hole from 10 feet, then both players birdied No. 11. Haas still held a three-shot lead, but horribly hit a 30-foot birdie putt at the 12th. He bogeyed the hole, while Watson birdied No. 12 to cut the margin to one.
Watson drew even with a 3-foot birdie putt at the 14th. Haas missed an 8-foot par putt on the same hole to finally trail Watson. The Senior British Open champion missed a 4-foot par putt at the 15th and the two were tied once again.
Both players birdied 16, then both missed reasonable looks at birdie on the par-3 17th. Watson's 8-footer never fell in the hole, while Haas missed from 2 feet closer.
Then, Watson made it to the winner's circle with a clutch putt at 18.
Quigley shot a 2-under 70 to tie for fifth place with Tradition winner Loren Roberts, who also managed a 2-under 70 on Sunday. The pair came in at minus-10.
Tom Purtzer posted a 3-under 69 and came in seventh at 8-under-par 280. Craig Stadler fashioned a round of 2-under 70 and finished eighth at minus-7.