Cook shot 4-under 67, holing a 15-foot par putt on the 18th hole to beat Michael Allen by two strokes.
Cook began the day a shot behind Allen, but birdied two of the first three holes to take the lead for good. Cook finished at 17 under and earned $440,000 for his fifth career victory on the 50-and-over tour.
Allen shot a 70 in the rainy, windy conditions that hampered his tee shots and forced the 2009 Senior PGA Championship winner to scramble most of the day.
Langer (69) shared third with David Frost (71) at 12 under.