Cochran's steady play on a wet course earned him a two-shot win over Mark Calcavecchia and his third overall seniors title, finishing at 12-under 276.
The 52-year-old's only career PGA Tour title came at the 1991 Western Open.
Calcavecchia, the 1989 British Open champion, was in contention until a four-putt double-bogey on No. 9. He carded a 3-under 69, finishing at 10 under 278.
Like Cochran, five-time British Open and three-time Senior British Open champion Tom Watson carded a 67, enabling him to grab a share of third place at minus-9 with Corey Pavin (69).