The Japanese player completed her first seven holes in 7 under, capped by an eagle on the par-5 16th, before finishing at 9 under for the day.
Hannah Green is the best-placed Australian and is tied for 14th after a five-under-par round on Thursday (Friday AEST).
Karis Davidson and Robyn Choi are one shot back in a tie for 26th, while their fellow Australian Minjee Lee is one shot further back again at 3 under and in a share for 40th.
The tournament at El Caballero Country Club — the tree-lined layout subbing for Wilshire Country Club for the second straight year because of course renovations — is the final event before the major Chevron Championship next week in Houston.
Former UCLA player Patty Tavatanakit was tied for second at 65 with Sei Young Kim and Suvichaya Vinijchaitham.
Iwai opened her morning round with a par on No.10, then birdied the next five and eagled the 16th.
"Good tee time in morning, so very peaceful and I feel comfortable," the 23-year-old said.
"I had a feeling so relaxing. I had a good feeling."
On her second nine, she added birdies on No.1 and 5. She matched the lowest score in the two years at El Caballero.
"A little bit thinking 58 or 59," she said. "But golf is not easy."
Iwai won the Mexico Riviera Maya Open last year for her first LPGA Tour victory. Twin sister Akie Iwai was second a year ago at El Caballero and won the Portland Classic last summer for her first LPGA title.
Akie Iwai shot 70 on Thursday, playing in the group ahead of her sister.
Green, the 2023 and 2024 winner at Wilshire, shot 67.
"I just feel very comfortable when I'm back here in LA," Green said. "Doesn't really matter if it's Wilshire."
The Australian has three worldwide wins this year — the HSBC Women's World Championship on the LPGA Tour along with the Women's Australian Open and Australian WPGA.
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