Watson, from Zimbabwe, 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.
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 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).
Watson won the AT&T Classic in March in California. Last year, he won the Senior PGA Championship and Boeing Classic.