Petrova will play Elena Dementieva in the last eight after her compatriot delivered a sure-footed performance to see off South African qualifier Chanelle Scheepers 6-1 6-3.
But 25th seed Anabel Medina Garrigues of Spain crashed out 1-6 6-4 6-0 to South African Chanelle Scheepers, while two-time grand slam champion Svetlana Kuznetsova, seeded 26th, lost 1-6 7-6 7-6 to Czech Iveta Benesova.
Eighth seed Victoria Azarenka was in excellent form in a 6-4 6-4 victory over Andrea Hlavackova of the Czech Republic and her next opponent will be South Africa's Chanelle Scheepers , who beat Russian Regina Kulikova 6-4 4-6 7-5.