The major-winning Australian, ranked No.10 in the world, had six birdies and one bogey, but will be kicking herself after a double-bogey on the 18th hole of her second round on Friday.
Green followed her opening 70 with a three-under 69 to sit in a share of 24th place at five under.
Defending champion Nasa Hataoka eagled the par-5 17th for a back-nine 30 and an eight-under 64 to take a one-stroke lead into the weekend.
Hataoka, who won in a playoff last year in a rain-shortened tournament, has a 36-hole total of 12-under 132.
Her Japanese compatriot Miyu Yamashita, who won last week's Maybank Championship in Malaysia, pulled her tee shot on the 18th fairway, which resulted in her only bogey of the day to shoot 67 and sit in second place.
Ana Belac, who became the first Slovenian player on the LPGA Tour in 2021, was tied for third after a 65, along with Japan's Fuka Suga (67), two strokes behind.
Hataoka, who has five top-10 finishes this season, grew up not far from the Taiheiyo Club Minori Course, northeast of Tokyo.
"I don't have a chance to play in front of so many Japanese fans, so I was really happy to be playing so well today," Hataoka said through an interpreter.
Of the other Australians in the field, Robyn Choi (71, 73) is tied for 63rd place at even par, while Minjee Lee is eight over after rounds of 77 and 75.
The Japan Classic is the last of four tournaments on the LPGA's so-called late-season Asian swing.
With AAP.
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