Fifth-seeded Carla Suarez Navarro of Spain and eighth-seeded Karolina Pliskova of the Czech Republic set up a semifinal meeting by winning their matches at the Diamond Games on Friday.
Suarez Navarro saved 10 break points in a 6-3, 6-2 quarterfinal win against former French Open champion Francesca Schiavone of Italy, who dropped her serve five times.
Pliskova defeated fourth-seeded countrywoman Lucie Safarova 7-6 (5), 6-3.
Both players hit eight aces each, while Pliskova saved four break points and broke Safarova's serve at the first opportunity in the second set.
In Friday's later quarterfinals, third-seeded Andrea Petkovic of Germany was playing No. 6 Dominika Cibulkova of Slovakia, and Germany's Mona Barthel took on Czech player Barbora Zahlavova Strycova.