Koch's 62, which was one stroke better than her previous low round, bettered the course record at Magnolia's Grove Crossings Course by two shots, despite play being contested under lift, clean and place rules.
'Obviously I hit some really good shots today and hit it close, but I also hit some good putts all day,' said Koch. 'You can go at these pins because the greens are receptive. You can hit a lot of shots close.'
Se Ri Pak, the 2001 champion, is alone in second place after a 7-under 65. Annika Sorenstam, who is looking for her fourth straight tour victory, Emilee Klein, Janice Moodie and Patricia Meunier-Lebouc are knotted in third at 6-under-par 66.
Koch missed birdie putts on one and three, but cashed in at the fourth with a 20-foot birdie. The shot of her round came at No. 5, when she holed a 5-iron from 170 yards out for an eagle-2.
'The pin was kind of back right and it's a downhill hole,' said Koch, a two-time Solheim Cupper. 'My caddie said that if you can just get it to the front, it will roll all the way back there. That's what I did. There was a ridge on the right and it came down toward the hole and then it disappeared.'
The Swede continued her fine play over the next two holes with a pair of 15-foot birdie putts. She made the turn at 5-under 31, but Koch still had plenty of birdies left in her bag.
Koch knocked a 5-iron to 10 feet to set up birdie at No. 11 and made it back-to-back birdies with a five-footer on the 12th. She wedged her third shot to five feet to set up birdie at the par-5 13th and played a beautiful 7-iron to six feet at the 14th to set up her fourth birdie in a row.
On 18, Koch landed an 11-wood 16 feet from the hole for her final birdie and her new low round on the LPGA Tour.
'It's not every day that you have three-footers and five-footers like today, but I also made some longer putts too,' she said. 'If I can keep playing steady and roll it good, then that's all I can do.'
Pak collected five birdies on the front nine, all of which came from 10 feet or longer. She added a five-foot birdie putt at No. 12 and broke out the pack at 6-under when she drained a 15-footer at the 17th.
'I don't play well in the first rounds, but on the weekend I have better scores,' said Pak, who shared the previous course record with Maria Hjorth and Sherri Steinhauer. 'I'm really happy today. I made a lot of good putts and I better play well because Annika is behind me.'
Sorenstam was flawless on Thursday with six birdies and no bogeys, but will need to go low over the next three rounds if she wants the single-season wins record on the LPGA Tour. Sorenstam has notched nine victories in 2002 and needs to win the final five events on the schedule to eclipse Mickey Wright's 1963 LPGA Tour record of 13 wins in a season.
Sophie Gustafson and Michele Redman share seventh place at minus 5.
Nancy Lopez, who is closing out her final full-time season on tour this week, shot a 4-under 68. She is part of a group tied for ninth that includes Karrie Webb, Meg Mallon and Lorie Kane.
Full-field scores from the Mobile LPGA Tournament of Champions