Pat Hurst was in the lead at her last hole but left with a double bogey and is alone in third place at 5-under par.
Jones opened on the back nine at Mount Vintage Plantation Golf Club and promptly knocked a 5-iron to 14 feet to set up birdie at the 10th. She eagled the par-5 12th but dropped a shot at the next when her 6-iron missed the green and she was unable to save par from five feet.
Jones righted the ship with back-to-back birdies at 14 and 15 for a 4-under 32 on her first nine.
The American birdied the par-3 third from eight feet but stumbled at the fourth when her 7-iron went over the green and she failed to get up and down.
Jones drained a pair of 20-footers for birdie at five and six, then made it three in a row when she played a 5-iron to four feet at the par-3 seventh. She was at 7-under par when she reached the par-4 eighth but Jones went over that green as well and never saved par, falling back to minus-6.
'I love this golf course,' said Jones. 'I played really well the last two days here last year. It sets up really well for me even though it is playing really long. I feel like I have the game to hit the shots.'
The 43-year-old has not won on tour since 2001 but Jones believes she still can compete on the highest level.
'I've been playing well all these years,' said Jones. 'I don't know what you're talking about. I haven't been winding down, I'm just getting ready.'
Gustafson, who played with Jones in the first round, took advantage of the par-5s on the back nine. She chipped to a foot to set up the tap-in birdie at 12 then chipped to 10 feet at the 16th for her second birdie.
Gustafson played an 8-iron to 15 feet for birdie at three. She tallied back-to-back birdies at six and seven and matched Jones in the lead with a 25-foot birdie putt at the ninth.
'I played pretty well,' said Gustafson. 'I managed to get up and down when I missed the green, so I didn't make any bogeys.'
Hurst was alone in first place at 7-under par when she made her way to the ninth, her final hole on Thursday. She had 12 feet for birdie but her putt slid by the right edge and rolled 30 feet past the hole. Her par putt came up five feet short and it was a double bogey and a round of 67.
'If you are standing out there, you can see what kind of pin placement it is,' said Hurst. 'You don't really have to talk about it because you can see how bad it was.
'I played well, hit the ball pretty consistent and made the putts. I made some putts out there where it could go either way, so overall I played pretty well.'
Laura Diaz, Lorena Ochoa, Wendy Ward and Giulia Sergas share fourth place at 4-under-par 68. Defending champion Janice Moodie, Nicole Dalkas, Catriona Matthew, Dorothy Delasin and Beth Bader are tied for eighth place at 3-under 69.