Watson, Tom Kite, Gil Morgan and third-round leader Jim Ahern were tied for the lead at 14-under after 17 holes.
After Morgan shot par on the hole, Watson's third shot from the bunker on the par-5 No. 18 at the Reserve Vineyards and Golf Club bounced right toward the hole.
He made his winning putt, wrapping the day up with a 3-under 69 for a 15-under 273, and retreated to the scorer's room to watch Kite and Ahern.
'I was ready for a playoff,' Watson said.
Ahern, known more for long drives than his putting, missed a 6-foot birdie putt on the 18th to finish with an even-par 72 and a 14-under 274.
Kite, the 1992 U.S. Open winner, missed a 5-footer that would have forced the playoff, ending the day with a 5-under 67.
It was Watson's second major this season on the Champions Tour; he also won the Senior British Open. It was his third career major on the senior tour.
Watson birdied the par-5 No. 15 hole under sunny skies but sometimes gusty winds as the Reserve. With the shot, Watson took a one-stroke lead over Morgan.
But on the next hole, Watson hit into the water and took a bogey to fall back to 14-under through 16 holes.
Morgan, a two-time winner of the Tradition, shot par on the final hole to finish with a 4-under 68 on the day, and in the group at 14-under for the tournament.
Morgan won in 1997 and 1998 at the Desert Mountain Golf Club. The Tradition moved to Oregon this year after 14 years in Arizona.
Ahern started the day with a one-stoke lead with a 14-under 202 after the third round, but had a roller-caster final round with four bogeys and an eagle.
Ahern, who noted he had never led - after any round - in a major before, won the Music City Championship in June, his second career win on the senior tour.
'I figured it would take 15 - someone in that group was going to finish at 15,' he said.
Morris Hatalsky, last season's rookie of the year on the Champions Tour who won the Columbus Southern Open earlier this season finished with a 2-under 70. He was at 13-under for the tournament with Bruce Summerhays, who shot a 66.
Watson finished with the group at 14-under as he rounded the corner - but he bogeyed the next hole.
He birdied the par-4 No. 12 to climb back into the co-lead, then made a well-placed shot from the bunker off the green of the par-3 14th hole to save par.
Kite had a chance to birdie the same hole and take the lead outright, but his putt stopped just short of the hole.
Watson was a four-stroke leader after the second round with a 10-under 62 - a record low round in the Tradition.
It was his sixth overall victory on the Champions Tour. He has won 39 times on the PGA Tour with eight majors.
Defending champion Jim Thorpe shot a 71 to finish three strokes back.
Jack Nicklaus, who has won the Tradition four times, was in contention most of the day, but bogeyed the par-3 No. 11.
It was the ninth and final tour event this season for Nicklaus, who was given a standing ovation by the gallery as he approached the 18th green. He finished four strokes back of Watson with a 70 on Sunday.