Quigley, who also won here in 2003, closed with a 6-under 66 despite a bogey at the 54th hole. Watson carded a final-round 70 at the Hualalai Golf Club.
'I came here to play well here and I did,' said Quigley. 'Tom played fantastic. I think the whole field was revved up to play well this week.'
After missing a par putt from just inside 5 feet at the 54th hole, Quigley watched as Watson missed a 9-foot birdie putt at the same hole that would have won the tournament. Watson tapped in for par and it was on to extra holes.
Watson missed the green and fairway at the first extra hole, No. 18. However he chipped to 6 feet and made the par putt. Quigley meanwhile found the green with his second shot, but two-putted for par from 12 feet.
Both players had lengthy birdie tries at the second playoff hole, No. 16 and each two-putted for par.
At the third extra hole, the par-3 17th, Quigley's tee shot came to rest in the fringe just over the back edge of the green. Watson's 8-iron flew over the green and came to rest in dried lava.
Watson took his penalty drop and chipped to 5 feet. Quigley rolled his birdie try 3 feet beyond the hole. Watson sank his bogey putt, but it was not enough. Quigley converted his short par putt to earn his ninth Champions Tour title after never winning a single event on the PGA Tour.
'I still consider beating Watson in Kansas City my greatest win out here,' Quigley said. 'I know he's been a great ambassador for golf throughout the world. To beat him is icing on the cake, but all 37 players who played here this week are fabulous players.'
Quigley got off to a hot start with birdies at Nos. 2 and 4. He stumbled to a bogey on the fifth, but came right back to birdie seven and eagle the par-5 eighth to get to 16 under.
Still trailing by two shots, Quigley birdied the 10th to get within one. Watson then bogeyed the 13th. Quigley then birdied par-5 14th to take the lead.
Watson, who carded 11 birdies on 12 chances on the par-5s this week, responded with a birdie of his own at the 14th to tied Quigley for the lead.
Quigley stiffed his second shot within a foot of the cup at the next. He kicked in that birdie putt to get to 19 under and the lead. He parred his next two holes to maintain that lead, but stumbled at the last.
The tour's ironman, who was playing in his 263rd consecutive event for which he has been eligible and 249th straight overall, missed a par putt from just inside 5 feet to force the playoff.
'I was blessed the with the ability to play good golf and I've got a great support group,' said an emotional Quigley. 'It's just unbelievable the twists and turns my career has taken. Fifty years basically as a club pro and I come out here win my ninth event out here.'
Watson got his round going with back-to-back birdies from the third. He climbed to minus-19 with a birdie at the par-5 10th. The five-time British Open champion faltered to his first bogey of the event at the par-4 11th.
Watson tripped to another bogey at the 13th, but atoned for the mistake with a birdie at the next. He parred his final four holes to join Quigley in the playoff.
'My nerves got to me a bit today,' admitted Watson, whose last win came at the 2003 JELD-WEN Tradition. 'I didn't feel comfortable the final few holes. I missed some putts on the back nine. I just didn't play well today.'
Hale Irwin (65) and Gil Morgan (67), respectively the 1997 and 1998 champions here, shared third place at 17-under-par 199. Wayne Levi and Mark McNulty tied for fifth place at minus-14. Craig Stadler was one stroke further back at minus-13 alongside Rodger Davis.
Tom Purtzer finished in ninth place at 12-under-par 204 after a final-round 69. Fuzzy Zoeller, the 2004 champion, and Peter Jacobsen ended in a tie for 10th place at minus-11.