Cornet ousted third-seeded Timea Bacsinszky 6-0, 6-4, losing 16 points over eight service games. Cornet dropped only 15 points total in the first set.
Ondraskova defeated sixth-seeded Roberta Vinci 6-4, 6-0 in 59 minutes. She lost eight points -- two on serve -- in dominating the second set.
Also Thursday, second-seeded Alexandra Dulgheru finished off a 7-6 (7-5), 1-6, 6-2 win over Anna Chakvetadze that was suspended Wednesday because of darkness before the third set began.
No. 4-seeded Anabel Medina-Garrigues topped Greta Arn 7-5, 6-3 and seventh-seeded Agnes Szavay beat Yvonne Meusburger 7-5, 6-3 in the other second-round matches.
Friday's quarterfinals schedule has Dulgheru going against Anastasija Sevastova, Szavay playing Cornet, Medina-Garrigues facing Ondraskova and eighth-seeded Polona Hercog meeting Patty Schnyder.
Copyright 2010 United Press International, Inc. (UPI).