In a mixed front nine at Liberty National Golf Club on Friday (Saturday AEST), world No.43 Kyriacou had bogeys on holes two, seven and nine, birdies on three and four and an eagle on the par-5 sixth.
The 24-year-old Sydneysider finished strongly in testing conditions with two more birdies on 17 and 18 to card a three-under-par 69 to sit joint-fourth at seven under, and the leading Australian.
"It was a little bit easier than I thought but not easy," Kyriacou, runner-up at last year's Evian Championship, said.
"I thought we were going to play through rain all day. I mean, I only had it for probably half the round in total, so wasn't as bad, but, yeah, it's not ideal.
"I guess back at home ... our winters aren't that nice, so where I play as well is right on the coast so definitely rainy and windy.
"I think that's also why I like playing in Europe, Scotland and stuff, because it kind of reminds me of home."
Compatriots Hira Naveed, Minjee Lee, Gabriela Ruffels, Hannah Green and Grace Kim all remain in the mix going into the weekend.
Naveed (69) is one shot adrift of Kyriacou, with Lee (71) another stroke back.
Ruffels (73), Green (72) and Kim (72) all sit at three under, while Karis Davidson (71) finished one under and one shot above the cut.
But not involved in Saturday and Sunday action are compatriots Sarah Kemp (74) at seven over and Cassie Porter (80) at eight over.
Those remaining in the event are chasing a leading trio including American duo Nelly Korda (68) and Andrea Lee (68) and Somi Lee.
South Korea's Lee had the equal-low round of the day, along with compatriot Jin Hee Im and Japan's Chisato Iwai, a five-under 67.
Korda, the defending champion and world No.1 who has yet to win this year, started her day on the back nine and erased two birdies on par-3 holes with back-to-back bogeys at the 17th and 18th.
After a birdie at the first, Korda made three more over her last five to make a late move up the leaderboard.
"After making two bogeys in a row you (need) to reset and just know that you have nine more holes to go and there is some opportunities out there even with the tricky conditions," Korda said.
"So just had a little bit of a mental reset and it worked."
First-round leader, and world No.2, Jeeno Thitikul of Thailand is in a group of six with Kyriacou at seven under after a 73.
Brooke Henderson (71), a two-time major champion and a former top-10 player, missed the cut, as did 2023 champion Rose Zhang (75).
With Reuters.
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