In a match of fine margins, it was Cornet that held her nerve when it mattered most, winning 76(2) 76(5) to reach her first WTA semifinal for nearly two years.
"It was a very difficult match and I'm so happy I could beat Anabel today because she's such a great player on clay," Cornet said. "But I just fought as hard as I could on every point.
"I played very well in both tie-breaks. The second set was especially close and I could have won easier but she came back and in the end I'm just really glad to make the semifinals here."
Next up for Cornet is compatriot Pauline Parmentier, who had an easier time of things in her quarterfinal against Alexandra Panova. After coming through qualifying, Panova took out No.5 seed Mona Barthel and recent Madrid semifinalist Lucie Hradecka in her first two main draw matches, but seemed to run out of gas against Parmentier, going down 63 63.
In the bottom half, No.2 seed Francesca Schiavone continued her serene progress through the draw with another one-sided victory, this time over Johanna Larsson. After Medina Garrigues' loss, Schiavone is now the only seed left standing and her 60 63 dismissal of Larsson suggests she will take some stopping.
"Yesterday was a long day as I didn't get on court until very late and at the beginning today my legs were quite heavy," Schiavone said. "It was closer than the score shows but I think I won the most important points.
"It's a good feeling to play these matches as I'm starting to feel my game better. I now have confidence to serve flatter and in my movement around the court."
Meeting Schiavone for a place in the final is Sloane Stephens, after the unseeded American saw off Ayumi Morita, 63 64. Stephens will be appearing in her first tour-level semifinal, but despite the disparity in experience, Schiavone is not overlooking her 19-year-old opponent.
"She is a young player who I like a lot. I think she is one of the best young players on the WTA," Schiavone added. "I will try to use my experience on clay against her, but I have to respect her as she has great shots and plays a lot off instinct and with confidence."