A tie against American Auston Kim was always going to be enough for Kyriacou to progress, and she duly halved the match with a spirited fightback at Shadow Creek.
A two-time European Tour winner and the 2024 Evian Championship runner-up, Kyriacou is still chasing a maiden victory in America.
But the 24-year-old is in with another shot after fighting back from three down through five holes on Saturday (AEDT) to secure the precious half point required to top Group 5.
Kyriacou will take on A Lim Kim for a place in the quarter-finals after the South Korean edged out compatriot Amy Yang 2 &1 to top Group 12.
But after winning their opening matches on Thursday, Kyriacou's countrywomen Minjee Lee, Gabriela Ruffels, Hira Naveed and Grace Kim were all eliminated.
Ruffels and Naveed were most unlucky after squaring off in an all-Aussie affair.
The victor was guaranteed at least a four-hole playoff against the winner of the other Group 3 match between New Zealand's world No.3 Lydia Ko and Spaniard Carlota Ciganda.
Alas the golf gods didn't smile on the Australians as Ruffels birdied two of the last three holes to claw back from 2 down to tie the match.Â
The half-point each was not enough as Ciganda instead scraped through with a 2-up win over Ko.
"Amazing," Ciganda said.
"I knew I had a really tough match, obviously, against Lydia Ko.
"She's not even just an amazing player, but such a good person.
"It's been a very great match, one of the toughest matches with the conditions - winds gusting - and it's just a really hard course.
"I'm just very happy. I played really good and happy to make it to the weekend."
Even with her newly-crowned PGA Tour-winning brother Min Woo turning up to support ahead of his Masters tilt, Lee never really had a say in her fate.
The dual major champion had to beat Patty Tavatanakit and hope Swede Madelene Sagstrom lost to her own Thai opponent Jasmine Suwannapuran.
Lee almost lived up to her end of the bargain, losing on the last after fighting back from three down with four holes to play, Sagstrom's 4 & 2 victory put paid to the West Australian's chances anyway.
Kim needed to beat Jenny Shin to have any hope, but lost 2 up to the American.
Korda had to defeat Ariya Jutanugarn, but lost 1-up as the Thai battled back after losing the lead on the 14th hole to progress.
Korda missed short putts on 15 and 16 and failed to make up the difference over the final two holes.
The American is still searching for her first victory this season, quite a contrast from a year ago when success at the Match Play was her fourth win from four starts, the first player in almost two decades to accomplish the feat.
Korda extended the streak to five two weeks later at The Chevron Championship to tie the LPGA tour record.
