MOBILE, Alabama, May 17, 2013 (AFP) - Korda built a 36-hole total of 13-under 131, while Australia's Webb climbed up the leaderboard with a bogey-free nine-under 63 for 132.
Chella Choi of South Korea led much of the day, but her six-under 66 finally left her in third place on 133.
Webb did all she could, grabbing four of her nine birdies in her last five holes as she closed her round with three straight birdies.
"I'm not sure the last time I had a bogey-free round, so I'm really happy about that," Webb said. "That's sort of been my problem is I have bogeys at the wrong time and it really kills momentum."
Webb predicted she'd need to maintain that kind of pace.
"I think I'll need to do that for the weekend playing with Jess. She played really solidly for two days," Webb said.
Webb has plenty of experience at Magnolia Grove Crossings Course, where she won the Tournament of Champions in 2000 before the course was overhauled.
"The greens are a lot more fair," she said. "But I liked the course the way it was. If you were on your iron game it really rewarded great shots. I think you can get away with some stray iron shots now, but I think it plays nicer."
Korda's lone career victory to date was a playoff triumph in the 2012 Women's Australian Open.
Back after a fortnight away from competition because of a wrist injury, the 20-year-old hit every fairway in regulation and all but one green.
"I feel really comfortable out here," she said. "I feel good."
Korda had four birdies on the front nine and three on the back. She had time to notice the charging round of second-year LPGA tour member Sydnee Michaels, whose 10-under 62 lowered the tournament record by two strokes and gave her a share of fourth place on 134, alongside two Thai golfers, Pornanong Phatlum and Thidapa Suwannapura, who both shot 65.
"Yeah, I saw Sydnee, I saw she was like eight-under through 12," Korda said. "Like, dang, that's getting it done today."
But Korda said she didn't feel pressure to respond.
"I kind of just went out here with really no mindset," she said. "Just come out here, try and hit good shots and convert when you can and kind of take your punishments when you have to."
First-round co-leader Lexi Thompson shot two-under 70 and was in a tie for seventh, four shots off the lead.
South Korea's Ji Eun-Hee, who shared the overnight lead, carded a 72 that left her six adrift.
Leading second-round scores on Friday in the Mobile Bay LPGA Classic (USA unless noted, par-72):
131 - Jessica Korda 66-65
132 - Karrie Webb (AUS) 69-63
133 - Chella Choi (KOR) 67-66
134 - Sydnee Michaels 72-62, Pornanong Phatlum (THA) 69-65, Thidapa Suwannapura (THA) 69-65
135 - Azahara Munoz (ESP) 71-64, Ariya Jutanugarn (THA) 69-66, Mina Harigae 67-68, Lexi Thompson 65-70
136 - Becky Morgan (WAL) 71-65, Paz Echeverria (CHI) 69-67, Nicole Castrale 67-69, Seo Hee-Kyung (KOR) 68-68
137 - Pak Jin-Young (KOR) 70-67, Kim Welch 70-67, Mariajo Uribe (COL) 70-67, Lisa McCloskey 69-68, Jennifer Johnson 67-70, Ji Eun-Hee (KOR) 65-72
138 - Shin Jiyai (KOR) 72-66, Sue Kim (CAN) 71-67, Katherine Hull-Kirk (AUS) 69-69, Nicole Smith 69-69, Beatriz Recari (ESP) 68-70, Park Hee-Young (KOR) 67-71