Further quotes and video footage from Konta's post-match press conference to follow after her doubles match.
Konta, the British number one world ranked 8, won 6-4, 6-1 and is the only one of the top four seeds remaining in the tournament.
Commenting on the fact she was playing her doubles partner when asked if it had been a problem, she said: "We are all adults, we must deal with that".
"That is something that happens with every player, it takes time to get used to a surface. I'm really happy to have made it to the end of the week!"
'It was hard, she started very strongly.
Konta had no idea she had reached that significant mark in her career which has seen her surge into the world's top 10 and also could not remember who had been her first "scalp" in 2007.
"It was definitely a nice little comeback", Konta added.
"I know Donna is playing very well recently and I know Lucie is a very unsafe player as well". "I'm looking forward to competing against one of them tomorrow".
The first yielded the Stanford title last summer, and she went on to reach the final of the prestigious Beijing Premier Mandatory last autumn.
The 20-year-old Vekic came through a close encounter with former Roland Garros finalist Lucie Safarova 7-6 (7/5), 3-6, 7-6 (7/4), after two hours and 50 minutes.
Rybarikova eliminated Alison Riske 6-2 6-7 (5) 7-5.
Safarova took a three-set victory over Tsvetana Pironkova of Bulgaria 6-3, 0-6, 6-4.
Konjuh will meet Natalia Vikhlyantseva in the semis, while Anett Kontaveit will play Lesia Tsurenko, who dumped out Kristina Mladenovic 6-3 6-1.