The two Americans shot 68s in the final round to finish at 13-under 203 with Mark O'Meara and Peter Senior at the Jack Nicklaus Golf Club Korea. O'Meara and Senior were eliminated from the playoff after bogeys on the third hole. Blake won with a 10-foot birdie on the fifth.
In April, Cook beat Blake in a playoff in Lutz, Fla.
"It's not like I was out to get revenge, but it's kind of nice to even the score and take him down," Blake said. "It's a big relief to win and feel like I can compete again and get it done."
Blake had a chance to win on the 18th hole in regulation but missed a 15-footer for birdie. Senior closed with a 64 to reach the playoff while O'Meara had a 67. Second-round leader Michael Allen shot a 75 and finished at 209.