Watson closed with a 3-under 69 to finish at 10 under. He earned $240,000 for his second victory of the year and fourth overall on the Champions Tour.
Never give up, Watson said. I hate this for Nick because we need him on the tour. This is my first time as the recipient of a back-in win.
Watsons drive on the 18th hole landed in the middle of the fairway, and he put his second shot 50 feet from the pin. His eagle putt slid 5 feet past the hole, but he holed the putt for what turned out to be the winning shot.
Price, who shot a 75 to finish at 9 under, appeared to be in control of the tournament through most of a clear and warm final round. But watery double bogeys on 15 and 16 dropped him out of the lead, and an 18th-hole par left him a stroke back.
Price tied for second with 2007 winner Scott Hoch (69) and Tim Simpson (70). Loren Roberts (74) was fifth at 8 under.
Watson won the AT&T Classic in March in California. Last year, he won the Senior PGA Championship and Boeing Classic.
Ian Woosman, of Wales, reacts
A stunned Price, still looking for his first Champions Tour win, said he was still unsure how his game unraveled.
This is such a crazy game, he said. I was hitting it so well today. I thought I could have closed my eyes on the 15th hole and made a bogey.
Price began the day with a two-shot lead over Scott Simpson and Roberts. He maintained the two-stroke edge with am even-par 36 on the front nine, but ran into double trouble with on 15 and 16.
On the par-4 15th, Prices 7-iron second shot found a tree hanging over the fairway that kicked the ball into a creek guarding the green. On the par-3 16th, which had already claimed plenty of final-round victims, his 5-iron tee shot hit on the bank and splashed back into the water when the wind switched.
His double bogey there left five players tied for the lead at 9 under' Price, Hoch, Tim Simpson, Scott Simpson and Roberts.
Price had one more chance to salvage a win or a playoff on the 18th, the second easiest hole on the course.
He hit a perfect drive, but his second shot found a greenside bunker. His chip left him 19 feet from the pin and he failed to covert the birdie putt.
It was pretty much over for me before then, Price said.