Minella ousted fourth-seeded Carla Suarez Navarro 6-2, 3-6, 6-3. She dropped serve at least once in each set but piled up six breaks in 13 receiving games in earning a spot in the quarterfinals.
Second-seeded Yanina Wickmayer needed more than 2 1/4 hours to get past Patricia Mayr-Achleitner 7-6 (7-4), 6-3. Wickmayer fought off nine of the 10 break points she faced but also converted just two of her own eight chances.
Ksenia Pervak, the third seed, had a much more conventional 6-2, 6-3 victory over Sarah Gronet. She lost just 10 points on serve and didn't have to deal with a break point.
Qualifier Chichi Scholl defeated sixth-seeded Irina-Camelia Begu 6-3, 6-4 while seventh-seeded Alize Cornet, who beat Sacha Jones 6-3, 6-2, and No. 8 Johanna Larson, who stopped Jill Craybas 6-2, 6-3, also moved into the quarterfinals.
Thursday's other results saw Estrella Cabeza Candela defeat Richel Hogenkamp 6-4, 6-3 and Yvonne Meusburger race past Dia Evtimova 6-2, 6-3.