She is now within one match of competing against sister Serena, who overcame China's Jie Zheng 6-4 6-2.
Third seed Jelena Jankovic played what she described as one of her worst matches as she crashed 6-2 7-5 to 16th seed Kaia Kanepi of Estonia.
The Serb could barely put a ball in court, and although she rallied from 0-4 in the second set to level at 5-5 she was unable to take the match into a deciding set.
"I think this is one of the worst matches in my career, to be honest," Jankovic, who surrendered the number one ranking to Serena Williams at the Australian Open, told reporters.
"For like 15 games I didn't put the ball on the court. For me it was horrible. My goal was to put two balls on the court and I couldn't do it. I never played a bad match like this before. I basically gave her the match. I played so badly it was tough for me to even be there on the court."
Virginie Razzano of France followed up her win over second seed Dinara Safina by beating Slovak Daniela Hantuchova 6-2 1-6 6-2 while holder Elena Dementieva of Russia eliminated Spain's Anabel Medina Garrigues 6-1 6-3.
Sixth seed Venus Williams was always in control against Cornet and was especially dominant early in the second set, surrendering just two points in four games from 1-1.
"I missed a few shots long and was a little upset about that but I managed to rein it in," the American told reporters. "She is obviously a really good player with a lot of potential.
"I'm sure she didn't play the way she wanted but I think I was able to put some pressure on her."
In a later match Serena struggled to gain an advantage over Zheng, but after forcing a backhand error to break for 5-4 she dominated the remainder of the match.
Eighth-seeded Serb Ana Ivanovic defeated Frenchwoman Camille Pin 6-2 7-6.
"I started really well. I was very aggressive in the first set then in the second I started pulling back a little bit on my shots," said Ivanovic.
"I got a bit frustrated and that causes more errors. But I'm very happy with the way I served at the end."
Fifth-seeded Russian Vera Zvonareva advanced after Frenchwoman Marion Bartoli retired with blisters on both feet when trailing 5-2 in the first set.
Russian qualifier Elena Vesnina went through 4-6 6-1 4-0 when 12th-seeded Slovak Dominika Cibulkova retired through illness.
