Bartoli had a walkover against Britain's Elena Baltacha and next plays eighth-seeded Lucie Hradecka of the Czech Republic. Petkovic earlier beat Zhang Shuai of China 6-1, 6-3 to set up a match against No. 5 Maria Kirilenko of Russia.
Petkovic fended off two break points in the first set and broke Zhang's serve twice in each set.
Kirilenko lost her serve five times before defeating Laura Pous-Tio of Spain 6-3, 3-6, 7-6 (5).
Former three-time champion Anabel Medina Garrigues of Spain, seeded seventh and a winner at the Estoril Open last month, booked her place in the last eight with a comfortable 6-2, 6-0 win over Serbia's Bojana Jovanovski.
Fourth-seeded Nadia Petrova of Russia also won, rallying to beat Alize Cornet of France 2-6, 6-2, 6-2. She will next face Daniela Hantuchova of Slovakia, who beat Mathilde Johansson of France 6-4, 6-2.