Green carded a two-under-par 69 to be tied for second entering the final round of the JM Eagle LA Championship in California.
The former major winner is seven under for the tournament, two shots behind American leader Cheyenne Knight.
The front-running pair are the only two players this week to shoot in the 60s in their first three rounds.
Green played her first 12 holes in three over but birdied five of her last six.
"The front was actually quite difficult," she said.
"It was a little bit of a different wind direction but it was also gusty, so picking the right moments for the club that you decide to hit was quite difficult.
"I knew there was some holes coming in that I could possibly make some birdies, but to birdie 17 and 18 was a really great finish and I'm really excited for tomorrow."
Green won the Vic Open and the Players Series Murray River in successive weeks last year in Australia but is chasing her first US victory since the Portland Classic in September 2019.
Knight had two birdies and an eagle in her third-round 67 on Saturday to pull clear of Green and South Korea's Hae Ran Ryu (67).
Scotland's Gemma Dryburgh fired a 66 to be six under and outright fourth, with Xiyu Lin (66) and second-round leader Aditi Ashok (72) another shot behind.
Green's fellow Australian Sarah Kemp (71) is sharing seventh at four under.
Steph Kyriacou posted a 69 to move back into red numbers at one under.
But Minjee Lee dropped back to level with par following a one-over 72.
Knight's best round of the week had special significance.
She shot 33 on the back nine. Her late brother, Brandon, who died in a car crash when Knight was 12, wore No.33 while playing high school football in Texas.
Knight teared up when an LPGA official mentioned her back-nine score.
"It's always special," she said. "I have someone up there watching over me. He's always with me."
- with AP
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