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Cook closed with a 5-under-67 at Hualalai Golf Club to catch Frost at 17-under 199. Cook made a 16-foot birdie putt on the 18th green.
Frost shot a 69, missing a 15-foot birdie putt at the 18th that would have given him a win in the Champions Tour season-opener. He had held the lead alone since the 12th hole of the second round.
"He is just really good and he's played really well, especially the last few months of last year," Cook said of Frost.
"He's won a lot of tournaments all over the world. He hit some beautiful golf shots today and didn't get much out of what he was doing and I hadn't either. It was kind of a survival day until it got down to the nitty gritty and you knew what you had to do."
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 20-foot birdie try.
Cook won $309 000 for his ninth victory on the Champions Tour, to go along with 11 on the PGA Tour. He birdied all four par-5 holes on Sunday, while Frost birdied just one.
"Overall I was in there all day," Frost said. "I hit a lot of great shots, but didn't capitalise on some of the great shots I hit. He (Cook) played really well, didn't miss any make-able putts."
Cook's victory gets him invited back next year. He did not have a bogey all week while Frost went bogey-free over his last 48 holes.
Bernhard Langer chipped in for a birdie 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.
Final scores:
199 – *John Cook 66 66 67, David Frost 65 65 69 (*Cook won on second playoff hole)
200 – Bernhard Langer 68 68 64
202 – Fred Couples 66 69 67
203 – Kenny Perry 67 72 64, Kirk Triplett 66 68 69
206 – Russ Cochran 67 70 69
207 – Tom Lehman 66 71 70
208 – Corey Pavin 68 71 69, Hale Irwin 70 68 70, Jay Haas 68 69 71, Steve Elkington 68 69 71, Tom Kite 66 69 73
209 – Joe Daley 69 72 68, Mark O'Meara 70 70 69, Willie Wood 66 72 71, Larry Nelson 69 70 70, Fred Funk 69 69 71
210 – Mark Wiebe 70 73 67
211 – Jeff Sluman 69 72 70
212 – Jim Thorpe 71 73 68, Loren Roberts 72 69 71
213 – Tom Watson 69 74 70, Jay Don Blake 71 72 70, Craig Stadler 70 71 72
214 – Olin Browne 73 71 70, Roger Chapman 70 73 71, Mike Reid 73 70 71
215 – John Huston 67 75 73, Mark Calcavecchia 71 70 74
216 – Brad Faxon 69 76 71
217 – Michael Allen 70 80 67, Dan Forsman 73 73 71, D.A. Weibring 71 73 73
218 – Eduardo Romero 73 73 72, Bruce Vaughan 73 72 73
220 – Curtis Strange 69 74 77, Bob Gilder 75 69 76
222 – David Eger 71 75 76
225 – Ben Crenshaw 78 74 73
