Cook and Blake shot 5-under 67s and are 9-under 135 heading into Sunday's final round at Jack Nicklaus Golf Club Korea. Mark O'Meara (69) and David Peoples (70), a co-leader after the first round, were a stroke back at 8-under.
Mark Calcavecchia (72), tied for the lead with Peoples and Allen Friday, dropped four shots in a five-hole stretch in the middle of the round and is tied for ninth at 6-under 138.
Calcavecchia is bidding to become the first player to win consecutive titles on the Champions Tour this season after capturing the Boeing Classic in Seattle three weeks ago.
The 36-hole leader has gone on to victory in seven of 19 54-hole tournaments on the Champions Tour this year.
"I didn't play the par-5s as well as yesterday but overall I thought I played quite well and was in control most of the day," said Allen, who played the par-5s 1-over compared to 3-under Friday.
"Tomorrow I have to beat the golf course to beat these guys," added Allen. "There are a lot of players very close, like Mark O'Meara and John Cook who is a good finisher when he's near the lead. I wish I'd gotten to 12- or 13-under and put some room between me and the rest of the field."
Cook and Charles Schwab Cup points leader Tom Lehman, both three-time winners this season, were among the players to shoot 5-under 67 in Saturday's second round.
"You have to peak at the right times and just go play," said Cook. "Hopefully this will be one of those weeks. My year has been interesting. I've had three really good weeks where I've won and then Westchester where I lost a playoff to Fred (Couples). I can't quite put my finger on the other weeks. They've just been average."
Canadian Rod Spittle birdied two of his last three holes to post the low round of the day, a 6-under 66, and jumped 17 spots to tie for sixth at 7-under 137 with Lehman and Bernhard Langer (67).
Chien-soon Lu, from Taiwan, landed the first ace of his Champions Tour career when he holed an 8-iron at the 156-yard 17th hole. Lu shot 70 and is tied for 20th at 2-under 142.
"Lucky shot," said Lu.