Parmentier eliminated Zheng 6-3, 6-4 by piling up six breaks over 10 receiving games. Zheng managed three breaks of her own but Parmentier claimed 55 percent of the points off Zheng's serve and cashed in 6-of-12 break-point chances.
Heather Watson also advanced on an upset, taking out sixth-seeded Anabel Medina Garrigues 6-7, (4-7), 6-2, 6-3 in a 2 1/2-hour battle. Watson had five breaks, with three coming in the final set when she won nearly 60 percent of the points.
Seventh-seeded Chanelle Scheepers dumped Mirjana Lucic 6-2, 6-2, winning more than 60 percent of the points off Lucic's serve; and No. 8-seeded Laura Robson topped Zhou Yi-Miao 6-4, 6-4 by finishing off five of her 16 break opportunities.
Watson and Parmentier are paired against each other in Friday's quarterfinals with Scheepers taking on Misaki Doi in the other match in that half of the draw. Also Friday, No. 1-seeded Samantha Stosur is to play Jamie Hampton and Robson is to meet Chang Kai-Chen.
Celebrity Families of 2014 [PHOTOS]