Second-seeded Alexandra Dulgheru of Romania overcame Tathiana Garbin of Italy 6-4, 4-6, 6-2 but unseeded Monica Niculescu of Romania upset third-seeded Timea Bacsinszky of Switzerland 6-3, 7-5.
"Except for a few forehand errors, I played well and had the match under control," Safarova said.
Safarova next plays Johanna Larsson of Sweden while Niculescu will face Czech Lucie Hradecka, who beat Stefanie Voegele of Switzerland 7-6 (6), 6-2.
Seventh-seeded Agnes Szavay of Hungary, fresh from winning her hometown Budapest title, also advanced with a 6-4, 6-3 victory over Liana Ungur of Romania.
In other matches, fifth-seeded Anabel Medina Garrigues of Spain routed wild card Kristyna Pliskova of Czech Republic, who won the Wimbledon title in the girls' singles, 6-1, 6-3 and Patty Schnyder of Switzerland rallied to beat wild card Zarina Diyas of Kazakhstan 6-7 (2), 6-4, 6-1.
Defending champ Szavay into Budapest home semisCech rejects Real link
