Minella parlayed three breaks over the second and third sets into a 3-6, 6-4, 6-3 win over Kanepi. She had a pair of breaks in the second set to even the match and followed by converting her only break chance in the third.
No. 5-seeded Kiki Bertens also went three sets but was able to come away a 7-6 (7-0), 4-6, 6-4 winner over Flavia Pennetta in a match that saw 14 breaks. Bertens took the match by finishing off all three of her break opportunities in the final set.
Sixth-seeded Francesca Schiavone broke open a tight match by winning eight consecutive games en route to a 6-3, 6-2 win over Simona Halep. The match was 3-3 in the first set when Schiavone won the next three games for the set. She then grabbed a 5-0 lead in the second set.
Also Thursday, seventh-seeded Kristina Mladenovic stopped Yulia Putintseva 6-3, 6-3; Lourdes Dominguez Lino beat ninth-seeded Tsvetana Pironkova 1-6, 6-4, 6-3; and Silvia Soler-Espinosa romped by Olga Puchkova 6-0, 6-3 in 58 minutes.
Friday's quarterfinals have Dominguez Lino taking on Bertens while Minella plays Soler-Espinosa. Also, third-seeded Alize Cornet is paired against Schiavone and Mladenovic goes against Chanelle Scheepers.