Cook closed with a 5-under-67 at Hualalai Golf Club to catch Frost at 17-under 199. Cook drained a 25-foot birdie putt on the 18th green.
Frost shot 69, not able to match Cook's birdie on the 54th hole of the Champions Tour season-opener.
Frost had held the lead alone since the 12th hole Saturday.
Both birdied the first playoff hole (No. 18) from inside 10 feet and went to the 17th tee. Cook hit his tee shot about 15 feet left of the hole and drained it after Frost had come up short with his birdie try.
Cook won $309,000 for his ninth victory on the senior tour. He did not have bogey all week while Frost went bogey-free over his last 48 holes.
Bernhard Langer chipped in on the last hole to finish third alone at 200. He started six back and bogeyed two of the first three before getting birdies on nine of the next 11 holes and finishing with a 64.
Fred Couples was five back going into the final round and also had two early bogeys. He rallied with an eagle and six birdies. That run died with a three-putt bogey at the 17th and he was fourth after a shooting a 67 and finishing at 202.
Kenny Perry was the first to make a move Sunday. He started the day in 14th place but surged into fifth with six birdies and an eagle. His 64 matched Langer's score as low round of the week. Perry finished four back with Kirk Triplett.
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