Green birdied the last two holes in carding a sizzling eight-under-par 64 on Thursday to sit solo second, a shot behind first-round clubhouse leader Jasmine Suwannapura.
Chasing a second LPGA Tour title of the year after snaring the LA Championship in April, Green racked up eight birdies in all without dropping a shot all day.
Kim earlier significantly boosted her chances of claiming the LPGA Tour's rookie-of-the-year award with a similarly brilliant start at Kuala Lumpar Country Club.
The rising star posted a flawless seven-under-par 65 to be equal third with Americans Gina Kim and Rose Zhang and Taiwan's Peiyun Chien.
Norway's Emily Kristine Pedersen and Mexico's Gaby Lopez fired six-under 66s to be three strokes behind.
Kim iced her round with her fifth birdie on the last hole, after also swooping a superb eagle on the short par-4 14th.
The 22-year-old entered the fourth-last event of the season in second position in the rookie-of-the-year race behind South Korean Hae Ran Ryu.
As well as capturing her maiden LPGA Tour victory at the Lotte Championship in Hawaii in April, Kim has enjoyed a series of top-15 finishes this year including at the Women's US Open and PGA Championship.
Fellow Australian Sarah Kemp opened with a three-under 69 to be tied 24th and safely in the clubhouse when the horn sounded to signal the suspension of play because of thunderstorms.
Steph Kyriacou is one stroke further back following a first-round 70.
The Australian quartet are bidding to follow compatriot Minjee Lee's victory last Sunday at the BMW Ladies Championship outside Seoul.
The world No.4 Lee is not playing this week.
But Thailand's Suwannapura has set a cracking pace with seven birdies and also an eagle at No.14 in her own unblemished first round on Thursday.
Play was suspended late in the day with 24 players, none of them threatening to take the lead, having to complete their first rounds on Friday.
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