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."
Watson's 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.
Watson won the AT&T Classic in March in California. Last year, he won the Senior PGA Championship and Boeing Classic.
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 an even-par 36 on the front nine, but ran into double trouble on 15 and 16.
On the par-4 15th, Price's 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.