Ariya was the only one to threaten but the Thai slipped back with two bogeys in the final six holes for a round of 70.
She was alone in second place, while defending champion Park Sung-hyun (71) and New Zealand's Lydia Ko (70) were equal third on three-under.
Near the wrong end of the field, Michelle Wie shot 82 on the back of her first-round 84.
The 29-year-old, reduced to tears on Thursday as she spoke about the impact of injury on her career, was attempting to play this week after taking two months off in an effort to allow bone chips and nerve entrapment in her right hand and wrist to heal.
"I was overly optimistic about how I could play this week and the status of my wrist," she said.
After Green's second shot at the 12th hole ended in a pond, she took a one-stroke penalty and assessed the options for her fourth shot.
"It was still quite a tough pitch shot," she said. "I said to my caddie, 'I need to get it close as possible'.
"I had to land it perfectly and I guess I did. I knew it was going to be close but I didn't think it had the chance of going in.
"When it went in I just laughed because with the hole-out (from a bunker) on seven yesterday and with the hole-out today, it's really going my way. So, yeah, just nice to at least be getting some luck on the course."
Green has not won on the LPGA Tour and has only one top-10 finish this year.
"I mean even when you play this type of golf at just a regular event you're pretty proud of yourself," she said.
"I've never put myself in this position in any event so to be doing it this week at such a great venue definitely shows things are going the right way.
"I have had some luck going my way. I hope that continues."
Former world No.1 Ariya, last year's US Women's Open champion, left her driver in the locker on Friday after putting it in the bag for the first round.
The long-hitting Thai, who rarely uses a driver, said she could probably do without it over the weekend.
"Maybe not because I feel I can punch it with my three-wood better."
Reuters