"It was definitely a tough start, starting off with a double bogey is never fun, but I really grinded out there", she said.
Chasing Kirk are a batch at six-under - Taiwan's Min Lee, Korean Chella Choi and American duo Marissa Steen and Jane Park.
Ko's even-par total was just one stroke inside the cut line, with Webb (3-over) missing out after a rollercoaster even-par round on Friday featuring four birdies and four bogeys.
"I think it would be my best win ever - as a kid you always dream about winning your national open".
Australia's top-ranked golfer Minjee Lee shot a three-under 70 on Friday to be four-under for the tournament.
Wie struggled through back spasms in the second round at Royal Adelaide, but she still managed to put herself in weekend position to make a run at winning her fifth LPGA title, her first in two-and-a-half years.
"I'm striking it pretty well, just need to get my momentum going".
Ko began the new LPGA season on Thursday with a first-round two-under par 71, which left the 19-year-old among a big group of players tied for 24th, six shots behind leader, Australian Katherine Kirk.
However, she was delighted to have comfortably made the cut in her first event on the world's biggest women's tour.
Kirk said her challenge now was to put more good rounds together to capitalise. His wife is leading the Open, and playing superbly.
"I was nervous last night trying to sleep but once I'd hit that first tee shot I felt good", said the former policewoman. I have just got to work a little harder. "I have just got to get my short game back to where it was in previous years, it's not quite where I want it to be".
Play resumes tomorrow at 7am at Royal Adelaide, with Jutanugarn at the head of those with morning tee times, due to start off the 10th tee at 7.44am.