Peng broke Sharapova twice in the first set, and then again in the sixth game of the second as the former top-ranked Russian appeared to show the strain of her three-set comeback victory over Victoria Azarenka of Belarus the night before.
"I've had matches where I didn't feel like I was maybe at the level that I wanted to be but I was able to fight through that and get through it, and today was just not one of those days, unfortunately," Sharapova said.
Sharapova did save two match points at 5-4 before losing.
The sixth-seeded Kuznetsova outplayed Bondarenko for much of the match and next faces Anastasia Pavlyuchenkova of Russia, who defeated Aleksandra Wozniak of Canada 6-4, 6-4.
Also, fourth-seeded Elena Dementieva of Russia beat Li Na of China 6-2, 6-0.
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.
Second-seeded Novak Djokovic trounced Viktor Troicki 6-3, 6-0 in an all-Serbian match, while Fernando Verdasco defeated Juan Carlos Ferrero 7-5, 6-4 in an all-Spanish encounter.
"Overall performance was very good," said Djokovic, who next faces Verdasco. "I was very patient with my shots and got a lot of returns back and made him make a lot of errors."