From six shots back at the halfway mark, Green soared into a tie for second, just two strokes off the pace, with a third-round five-under-par 67 on Saturday (Sunday AEST).
Champion in 2023 and 2024, Green looked little chance of reeling in Sei Young Kim before the South Korean invited the chasing pack back into the $US3.75 million tournament with four bogeys in her last five holes.
Kim had been seven shots clear of the field before her late stumble, but still holds sway at 15 under after following up a pair of 65s with a third-round 71.
"Oh, wow, it feels like roller-coaster," the 33-year-old Kim said.
"It's golf. It can be happen again. It's learn and then learn and learn. Mistake and then learn. Hopefully success end of the day tomorrow."
Green holds a share of second with Thailand's Suvichaya Vinijchaitham (67), American Jessica Porvasnik (68) and Korean Ina Yoon (71).
"I didn't hit many greens. Felt like I really had to scramble today," Green said.
"It was nice, I did have a chip-in, and the rest the shots I had I kind of left myself all right positions."
Australia's world No.8 is among the game's form players, boasting three worldwide wins this year and has carried her A-game to Wilshire Country Club.
The 29-year-old is bidding to add a third LA Championship trophy to her hat-trick of victories at the HSBC Women's World Championship in Singapore on the LPGA Tour and the Women's Australian Open and Australian WPGA.
"I don't really know where they put the pin locations for tomorrow, but I'm sure they'll be tricky and there will be some holes that will probably play easy," Green said.
"I've noticed the last two days the wind is kind of switched at times, so that will be tricky to manage. The ball is going far off the tee."
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