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
Petrova holds off Bondarenko at Ponte Vedra
MLS Original Marsch honored by Chivas
