Lonnie Nielsen, who earned his card on the elder circuit through Q-School, is alone in second place at 9-under-par 63.
Champions Tour stalwarts Hale Irwin and Larry Nelson are tied for third place after opening with rounds of 7-under-par 65.
Koch's 62 on Friday broke Jay Overton's previous mark from last year by a shot. The 62 was also Koch's lowest on either the Champions Tour or PGA Tour as he posted 63 four times on the PGA Tour, most recently at the 1986 Southern Open.
'I wish this day would never end,' said Koch. 'It was one of those runs today where you're in that zone. It will be an interesting challenge tomorrow. This is the first time I've been 10 under par.'
Friday's opening round was delayed two and a half hours because of heavy fog. When play started, the threesomes went off split tees and everyone in the field was able to complete their round.
Koch collected three birdies and a bogey on his front nine to make the turn at 2 under par. The NBC commentator caught fire on the back nine and that led him to his career round.
Koch soared up the leaderboard with back-to-back birdies at the 11th and 12th from two and five feet, respectively. He drained an 18-footer for eagle at the 13th and birdied No. 14 to match Irwin and Nelson at 7 under par.
At the par-3 16th, Koch knocked an eight-iron to three feet to set up birdie and take the lead at minus-8. He drove in the fairway at the par-5 17th then hit his second into a greenside bunker. Koch holed out from the bunker for an eagle to get to 10 under par.
Koch parred the difficult closing hole to polish off his best round as a professional.
'All of a sudden on No. 11 things started to happen,' said Koch. 'When I hit that shot on No. 17 I knew it was a good shot but I was not sure it was going in.'
Nielsen only went 1 under on the front nine, but like the man ahead of him on the leaderboard, took off on the back side. He eagled the 13th and birdied every other hole but the 12th and 17th.
'I'm still not comfortable with my golf swing yet,' admitted Nielsen. 'We had a great day to play today. This course is right out in front of you.'
Gil Morgan got to 7 under par but dropped a shot at the eighth, his 17th of the round. He finished with a 6-under 66 and is tied for fifth place with Don Pooley, Morris Hatalsky, Leonard Thompson and Tom Jenkins.
Craig Stadler, John Harris, D.A. Weibring and Mike McCullough share 10th at minus-5.
Jack Nicklaus, the architect of TwinEagles, carded a 4-under-par 68 and is part of a group tied for 14th.
Vicente Fernandez, the 2003 champion, opened his title defense with an even- par 72 and is tied for 47th place.