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.
Swim Week Miami Beach 2014 [PHOTOS]