Cook's overall score was 11-under 205.
"Wind was coming from a different direction and it was tricky," Cook said. "I've had trouble finishing events this year and I did that today."
The victory was his third on the Champions Tour.
Tway (70) and Haas (71), who won the tournament in 2006, ended up at 207.
First- and second-round leader Dan Forsman carded a 73 and shared fourth place at 208 with Tom Lehman (68) and Bernard Langer (69), who won the event the previous two years.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Costly malfunction causes beer flood at Boston-area brewery