Errani fought off Eugenie Bouchard 7-6 (7-4), 6-2 to run her year's match record to 14-7. She is seeking her first championship of the year and the fourth of her career.
Her quarterfinal opponent will be fifth-seeded Kiki Bertens, who had no trouble defeating qualifier Maria Jose Martinez Sanchez 6-1, 6-2.
Two players reached the quarterfinals when their opponent was forced to retire.
Silvia Soler-Espinosa moved on when fourth-seeded Irina-Carmelia Begu abandoned their match in the second set. Maria-Teresa Torro-Flor also retired in the second set against No. 7 seed Lourdes Dominguez Lino.
In addition to the Errani-Bertens quarterfinal, Thursday's matches will find Cornet meeting Dominguez Lino, Knapp playing Soler-Espinosa and Schiavone facing Suarez Navarro.