From 4-2 down in the first set against Karolina Pliskova, the second-seeded Cornet lost just two more games the rest of the way in her 76(4) 60 victory that saw her convert on five of six break point chances and lose just seven points on her first serve.
"I'm happy to be back in the quarterfinals here in Guangzhou," Cornet said. "It was a tough match today, especially in the first set when I was down a break twice. She was serving very well and I was lucky to win it. I'm feeling great here in China and want to go further in the tournament."
Cornet's foe in Thursday's quarterfinals will be Yvonne Meusburger.
"I haven't played against her in a long time," Cornet said. "She's a very good player, a fighter. She doesn't miss a lot of balls. I will have to play aggressive and go for it. She's not going to give it to me. It's going to be a tough battle, but I'm ready for it and I really want to reach the semifinals."
As for Robson, she was a 63 76(4) winner over Zheng Saisai to make her first WTA quarterfinal of the year. Next up for the third-seeded Robson is another Zheng, Zheng Jie, who rallied from a 5-0 first set deficit for a 75 76(1) triumph over Timea Babos.
"I have to play better than I did today for sure," Robson said. "She's playing well. I saw some of her match today against Babos. It's going to be a tough one."
Another Brit also moved on, with qualifier Johanna Konta advancing to her first WTA quarterfinal by defeating No.4 seed Peng Shuai, 61 63. And in another upset, Zhang Shuai beat No.6 seed and defending champion Hsieh Su-Wei, 62 62, for her first win in four matches in their series.
Also victorious were eighth-seeded Monica Puig and qualifier Vania King, who lost nine straight games at one point but still got the best of newly crowned Tashkent champ Bojana Jovanovski, 64 06 64. Later in the day, King and Galina Voskoboeva were the first to secure a doubles semifinal berth.