Seeking her maiden LPGA title, 24-year-old Sydneysider Kyriacou continued a strong campaign at treacherous Shadow Creek when she beat A Lim Kim 2 and 1 in the round of 16 on Saturday morning.
But the two-time European Tour winner finally succumbed when American Solheim Cup star Lauren Coughlin prevailed 1 up in their afternoon quarter-final.
Kyriacou made a great start and was three up after just four holes. However Coughlin fought back mid-round, winning three straight holes from the ninth hole to be tied.
The par-3 17th hole proved decisive as Coughlin won with a par to go 1 up after nearly holing her tee shot while Kyriacou narrowly missed the green and could not get up and down.
Coughlin then triumphed with a par at the 18th to set up a semi-final against Thailand's Ariya Jutanugarn on Sunday.
Coughlin has played each at least 18 holes in every match.
"I'm definitely feeling it in my legs, and I think I was a little bit tired to start the first few holes," Coughlin said.
"Then the adrenaline started to take over there probably through about 8 or 9. I finally started to mentally feel like I was back in it."
Jutanugarn downed Sweden's Maja Stark 4 and 2 in their quarter-final a day after taking down world No.1 Nelly Korda.
American Angel Yin will have to wait to learn who she faces in the other semi after she defeated second-ranked Jeeno Thitikul 4 and 2.
Having survived 28 holes in the round of 16 to beat Ashleigh Buhai in the longest match in the five-year history of the event, Frenchwoman Celine Boutier returned to 30 minutes later for her quarter-final against Madelene Sagstrom.
But their match was finally suspended because of darkness with the players tied through 17 holes.
"Yeah, it was a very long day," Boutier said. "I feel kind of tired, but I feel like it was a good match again this afternoon, very tight and going back and forth with Madelene. So just got to keep pushing until tomorrow."