Donna Andrews also carded a 68 and Becky Morgan, from Wales, shot a 3-under 69 in the second round to join Neumann in first at Mount Vintage Plantation Golf Club. The trio is knotted at 8-under-par 136.
Cristie Kerr, a three-time winner this season, posted a 4-under 68 and shares fourth place with Jeong Jang (67) and Laura Davies (69). The group is tied at 6-under-par 138.
Neumann, a Swede who has played on six Solheim Cup teams, opened on the back nine Friday and broke into red figures with a 20-foot birdie putt at the 12th. She hit a poor approach at the par-4 14th, finding the greenside bunker, but she holed out from the trap for her second birdie.
At the par-4 17th, Neumann hit an 8-iron to 15 feet and drained the birdie putt. She made it two in a row with a 17-footer at No. 18.
Neumann kept her strong play going on the second nine. She ran home a 25-foot birdie putt at the first and tallied her fourth birdie in a row at two, when she sank a 30-footer.
'It's a bucket today,' said Neumann, referring to the size of the hole during her strong putting performance around the turn. 'Everything is dropping. Even though they were long, they were easier to read.'
Things fell apart quickly for Neumann, who won the 1988 U.S. Women's Open. At the fourth, her tee shot found a fairway bunker and her second landed in a greenside trap. She could not get up and down for par and missed the green at five. Neumann once again could not save par at the hole and fell into a tie for the lead.
'I have been putting really well these last two days,' said Neumann. 'I think yesterday I probably played better than I did today. But I made some crucial putts today to keep the momentum going, and I'm just very pleased to be 8 under par.'
Andrews hit a 9-iron over the green at the second hole, then missed her 4-footer to save par. She rebounded from there with a 15-foot birdie putt at the fourth.
Andrews had 50 feet for birdie at the par-5 ninth and after a few seconds of hanging on the hole, the putt dropped in the cup. She made it two in a row at 10 when she made a 20-footer, but things soon fell apart.
She bogeyed the 12th and 13th holes when her approaches missed the green in regulation. Andrews came back with three birdies in a row from the 14th, including a 40-footer at No. 15 to get a piece of first.
'I had a couple that got away from me today, but obviously I made a lot of putts,' said Andrews, who won the 1994 Kraft Nabisco Championship. 'I made some really long putts today and that was how I was able to score as well as I did.'
Morgan had a much calmer round compared to her fellow co-leaders. She opened on the back nine and birdied the 11th when her 11-wood stopped 8 feet from the hole. Morgan made a 15-footer for birdie at the 15th to reach 7 under par and joined the leaders with a birdie at the par-5 sixth hole.
While Neumann has 12 LPGA Tour wins and Andrews half that number, Morgan, 30, is winless since joining the circuit in 2001. She does not see her inexperience as a problem.
'Hopefully I'll play the way I have the last two days,' said Morgan. 'I kind of feel like this is about the best I've played all year. It's been pretty steady stuff.'
Beth Daniel (68), Joanne Morley (72) and Miriam Nagl (70) are tied for seventh at 5-under-par 139.
Grace Park and Kim Saiki, two of three first-round co-leaders, only managed 2-over 74s on Friday and are part of a group tied for 10th. Amateur Ya-Ni Tseng (69), Patricia Baxter-Johnson (70), Soo Young Moon (71), Joellyn Erdmann-Crooks (70) and Maggie Will (69) joined Park and Saiki at minus-4.
Silvia Cavalleri, the other co-leader with Park and Saiki, struggled to a 4-over 76 and is part of a group tied for 24th at minus-2.