Petrova overcame 71 unforced errors with the help of seven aces. She is coming off a "stress reaction'' injury to her right foot and played with both feet taped.
She will play Saturday against fifth-seeded Aleksandra Wozniak of Canada, who outlasted Tamira Paszek of Austria 6-3, 3-6, 7-6 (9-7).
Petrova led in the tiebreaker, but Bondarenko hit a forehand winner and Petrova put a forehand into the net to make it 6-5. Bondarenko lost when she hit a backhand into the net.
"I will gain confidence from this and that is what I have been lacking,'' said Petrova, who developed blisters on her feet during the match.
"I just want to put them in a bucket of ice,'' she said.
Third-seeded Dominika Cibulkova lost to Elena Vesnina 7-5, 6-7(5), 6-3.
Vesnina needed four match points to subdue Cibulkova. Two of the lost points were of her own doing when she put a forehand into the net and was wide on a cross-court effort.
"From my side it was not good,'' Cibulkova said. "I didn't feel good on the court and I don't know why. I was fighting and fighting and when she went up 3-2 (in the third set) I got panicked and played stupid again.''
Wozniak blew a 5-2 lead in the third set and double-faulted on her first match point before ousting Paszek.
The Canadian, nursing an injury to her right shoulder, led 6-5 in the tiebreaker before the double-fault. After an exchange of points, Paszek put two balls wide to give Wozniak the win.
"I got tight and that's what led to the double-fault,'' Wozniak said. "But you have to fight your nerves and just stay strong, especially in a tiebreaker.''
In doubles, Taiwan's Chia-Jung Chuang and India's Sania Mirza beat Petrova and Bethanie Mattek-Sands 6-4, 7-5. Chuang and Mirza will meet Liga Dekmeijere and Angela Haynes in the semifinals.
Petrova holds off Bondarenko at Ponte Vedra
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Petrova holds off Bondarenko at Ponte Vedra
