The sixth-seeded Russian outplayed Bondarenko for much of the match and next faces Anastasia Pavlyuchenkova of Russia, who defeated Aleksandra Wozniak of Canada 6-4, 6-4.
Nikolay Davydenko of Russia advanced in the men's field, easily beating Philipp Kohlschreiber 6-1, 6-0. Davydenko will next face Marin Cilic of Croatia, who beat Julien Benneteau of France 6-2, 2-6, 6-0.
Later, Maria Sharapova of Russia will face Peng Shuai of China, and Li Na of China plays Elena Dementieva of Russia.
On the men's side, Novak Djokovic will play Viktor Troicki in an all-Serbian match, and Fernando Verdasco faces Juan Carlos Ferrero in an all-Spanish encounter.