Goerges beat Garbine Muguruza Blanco 7-5, 5-7, 6-2 as the Spaniard's erratic serve let her down with 14 double faults in the 2½-hour match.
Cibulkova rallied for a 5-7, 6-4, 6-4 victory over Klara Zakopalova in another long match that featured a combined 17 break points. But the Slovak bounced back from a first-set deficit to beat her Czech opponent on the outdoor clay.
Cibulkova faces Sorana Cirstea next after the Romanian player beat Lourdes Dominguez Lino of Spain 1-6, 6-3, 6-1.
Yuliya Beygelzimer of Ukraine joined Cibulkova in the last eight after edging fifth-seeded Flavia Pennetta of Italy 6-2, 6-7 (5), 6-4.
Qualifier Olga Govortsova needed more than 3 hours to beat Laura Pous-Tio 7-6 (4), 6-7 (6), 6-2.
Govortsova knocked out top-seeded Francesca Schiavone on Tuesday. She overcame errors to beat her Spanish opponent.