Bidding to become only the second South African to win a women's major, Buhai went clear with a wonderful seven-under-par 64 third round at historic Muirfield on Saturday.
The 33-year-old overcame windy conditions to record eight birdies - including four straight on holes Nos. 4-7 - before settling for a bogey on No.18 to be 14-under.
"Yeah, obviously I'm very pleased," Buhai said. "To be able to shoot that score in those conditions, you have to be able to pat yourself on the back; so much so that I thought I was 6-under, not seven."
First-round leader Hinako Shibuno shot a 66 and second-round leader In Gee Chun had a 70 and the pair are tied for second.
Seven-times major champion Inbee Park (70) and Sweden's Madelene Sagstrom (71) are tied fourth, a further two shots back.
World No.2 Lee (70) and young gun Kyriacou (70) are next, tied with Japan's Miyu Yamashita (71) at five under, but a distant nine shots behind Buhai.
Lee is guaranteed the world No.1 ranking if she win's the Open, or is runner-up and Nellie Korda doesn't finish higher than third.
Chasing a third major title and second for the year, Lee mixed four birdies bogeys with three birdies in her round while Kyriacou did likewise.
They will need to hope Buhai struggles with leader's nerves in windy conditions which she has made light of for the past two days.
"The position I'm in and considering how many shots back I am, I think I can be aggressive and I can just try and make birdie every single hole," said Lee.
"Ash, she has probably contended a few times but it's the British Open and the final group, so I'm sure she'll have a few nerves.
"I'm going to have to shoot a really low score and hope for her to come back a little bit."
Kyriacou was of like mind.
"I will definitely be more aggressive," she said. "I'm a few shots back. I mean, it's not impossible but it's going to be harder.
"Just like going for pretty much every pin that's not silly. Just backing myself. What's the worst that could happen? I shoot 10-over, big whoop."
Fellow Australian Hannah Green dropped back to tied 19th with a 74 featuring six bogeys, with Whitney Hiller is tied 41st at one over.
Buhai, who had a 65 on Friday, has yet to win on the LPGA Tour, although she has been victorious three times on the Ladies European Tour. The 33-year-old does have two top-10 finishes in 2022.
She is looking to join Hall of Famer Sally Little (1980, 1988) as the only South African woman to win a major.
The South African also led this tournament in 2019 at Woburn after the second round but finished fifth, her best result at a major.
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