McHale rallied past Misaki Doi in their second-round match 4-6, 6-4, 6-4 to earn a quarterfinal meeting with No. 1 seed Marion Bartoli.
McHale has improved from a world ranking of 42nd at the start of the year to a current position of 27th. She reached the third round of each of the year's first three major championships.
Second-seeded Dominika Cibulkova also advanced, routing Marina Erakovic 6-2, 6-4. Cibulkova will take on Urszula Radwanska in the quarterfinals after Radwanska coasted past Melanie Oudin 6-2, 6-1.
Jelena Jankovic was the last to reach the quarterfinals, doing so with a 2-6, 6-4, 6-4 decision over Melinda Czink.
Jankovic's next opponent will be qualifier Yung-Jan Chan, who earned a spot in the quarterfinals Wednesday.
Celebrity Families of 2014 [PHOTOS]