The 23-year-old Sydneysider shot the lights out early on the Bay Course at Seaview Resort to be tied fourth, four strokes behind runaway leader Arpichaya Yubol.
Kyriacou posted birdies on the first, third, fourth and fifth holes before adding to her tally on the 10th, 15th and 18th. Her lone bogey came on the par-four 12th.
It proved to be a good day all round for the Australian contingent with Robyn Choi (66) and Hira Naveed (67) also in contention.
But it was all about Yubol, who followed a career-best finish on the LPGA Tour with a career-low 10-under 61 on Friday for a two-stroke lead over Jenny Shin.
The 22-year-old Thai player, who finished fifth in last week's US Women's Open, had eight birdies and a chip-in eagle playing in the calm morning conditions.
With a 60 within her grasp, Yubol narrowly missed a 10-foot birdie putt on the par-5 ninth hole, her last of the day.
Australian Hannah Green is the only other player to shoot 61 this year, doing it at par-72 Seville in Gilbert, Arizona, in March.
"I feel like I just start to play golf, like happy golf like every hole," said Yubol, who won as a professional in Thailand.
"Because I feel like my confidence is coming back from last week in the US Women. It was the greatest week in my life and then it makes me more confident for this week."
Yuka Saso followed up her second US Women's Open title with a 69. Hinako Shibuno, who was runner-up last week to her Japanese countrywoman at Lancaster Country Club in Pennsylvania, opened with a 66.
Yubol's 61 matched the tournament record shared by Sei Young Kim and Sakura Yokomine in 2018. Annie Park ended up winning that year.
Shin, who has one win since joining the tour in 2011, played in the afternoon with stronger wind. She had nine birdies and bogey.
"Well, the fact that every hole is birdie-able, compared to last week, just helped a lot," Shin said. "A little bit easier just kind of going after the pin, which I didn't do at all. So, yeah, it was fun. That was the biggest difference: It was fun."
Narin An, a two-time winner on the Korean LPGA, is seeking her first US victory.
An shot a bogey-free 64 and is three shots back while 38-year-old Brittany Lincicome, whose eight tour wins include this event in 2011, had her best round of the year playing with a new putter and was part of a large group at 65.
Brooke Henderson, who won this event two years ago, also shot 65 alongside Kyriacou, Nasa Hataoka, Megan Khang and amateur Rachel Kuehn, a 22-year-old from Wake Forest, who overcame a bogey-bogey start.
Defending champion Ashleigh Buhai shot 67.
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