"It took everything," Oudin said of the 2-hour, 27-minute match. "I started off not exactly like I wanted to, losing the first 10 points of the match, and I was looking forward to winning a point."
After dropping the opening set, the eighth-seeded Oudin took a 3-0 lead in the second before Peng fought back.
"From there it was neck and neck the rest of the way," Oudin said.
A key moment for Oudin came at 5-all in the second trailing 0-40 and she rallied to win.
"That was a huge game to win because she would have been serving for the second set," Oudin said.
She will next face fourth-seeded Elena Vesnina of Russia in the quarterfinals. Vesnina beat German Julia Goerges 6-3, 6-2 earlier in the day.
Vesnina fell behind 3-2 in the first set but won 24 of the next 26 points to close out the set and take a 2-0 lead in the second. At 4-1 in the second a wind gusting to more than 25 mph played havoc with the Russian.
"I was hitting against the wind and she was hitting so hard and the ball was heavy," Vesnina said. "I was trying to hit it, but it was not flying to the baseline."
Goerges began the seventh game of the second with a pair of aces before play was delayed nearly 10 minutes when a fan passed out in the stands and was treated. When play resumed, Vesnina won four consecutive points for a 5-2 lead in windy conditions.
"It's scary," Vesnina said. "(The delay) helped me a little bit, actually. She served me two aces in a row and the lady passed out and I can tell her thank you, actually. I saw the doctor and he told me she was fine now."
Varvara Lepchenko, who got in the tournament as a Lucky Loser when Virginie Razzano withdrew, advanced to the quarterfinals with a 6-1, 6-1 win over Anne Kerber. Olga Govortsova, of Belarus, won 71 percent of her first-serve points in beating Georgia's Anna Tatishvili, 6-2, 6-2.
In doubles, Goerges and Barbora Zahlavova Strycova lost to Sarah Borwell and American Raquel Kops-Jones, 6-3, 3-6, 10-8.
Primera Liga round-upWawrinka, Hanescu win at Casablanca
