Other seeds in action were No.12 seed Kateryna Bondarenko, a 46 64 75 winner over lucky loser Melinda Czink, and No.17-seeded Aiko Nakamura, who fell to British wildcard Melanie South, 26 64 64.
"I started off a little bit nervous but I had belief in myself," said South, who reached her first ever Tour quarterfinal. "Nakamura is very experienced, but I kept serving well. I have a very aggressive game and it paid off. When it got to match point and Nakamura was serving I decided to go for it. I'll learn from it in the future and hopefully I'll even be able to close the match out a game earlier."
South will face Wickmayer in the quarterfinals in the hopes of becoming just the third British player to reach the final four in this event's history. Anne Hobbs achieved the feat in 1984 and Jo Durie did it in 1992.
"I believe I can beat anyone here," South continued. "I have a good game on grass and I have a good serve. But so does Wickmayer."
In other matches, Petra Cetkovska beat Camille Pin, 64 67(5) 63; Marina Erakovic beat qualifier Yaroslava Shvedova, 63 75; and Bethanie Mattek beat Tamarine Tanasugarn, 64 62.
All four quarterfinals will take the courts at the Edgbaston Priory Club on Friday, pitting Vaidisova against Mattek, South against Wickmayer, Alona Bondarenko against Erakovic and Kateryna Bondarenko against Cetkovska