Bartoli, seeded fourth this week, roared past Aleksandra Wozniak 6-2, 6-2 in less than an hour. She had five breaks while winning 70 percent of the points on serve.
She next goes against seventh-seeded Lucie Safarova, who eliminated local favorite Heather Watson 7-6 (7-5), 6-1. Safarova won 69 percent of the points in the second set despite dropping her serve.
No. 5-seeded Angelique Kerber was only the third seeded player to reach the quarterfinals. She defeated Chanelle Scheepers 6-3, 6-2 by piling up seven breaks in Scheepers nine games serving.
Tamira Paszek ousted eighth-seeded Daniela Hantuchova 6-4, 3-6, 6-1 and Klara Zakopalova stopped No. 9-seeded Petra Cetkovska 6-1, 1-6, 6-2.
Pironkova is paired against Paszek in the same half of the draw as the Bartoli-Safarova match. Also, Kerber faces Makarova and Zakopalova draws Pavlyuchenkova in other quarterfinal matches Thursday.