France’s Cornet claimed the first set on a tie-break before Azarenka recovered to secure a 6-7 (2-7) 6-3 6-2 and set up a fourth-round clash against Ana Ivanovic.
“I don’t think I played my best tennis today for sure, but I have to give her credit,” said world No2 Azarenka. “She played really well.
“The dynamic of the match was a little bit weird for me. I felt like I didn’t take my opportunities in the first set, which was kind of a waste, and it gave her a lot of confidence. She really came up with the great shots when she needed with the big serves.
“I actually have never seen her serve like that before, so that’s definitely a big improvement from her side.”
The 24-year-old added: “I’m glad that I could turn things around in the second and third set. There was more me playing, more finding the rhythm. I felt much better in the third set than in the first set. It’s pretty good, so I’m happy with that.”
Elsewhere in the women’s draw, Petra Kvitova, suffering with a fever, lost to world No81 Alison Riske 6-3 6-0 in just 65 minutes.
And Caroline Wozniacki stuttered to her fourth loss of the year to a player ranked outside the top 100 as qualifier Camilia Giorgi advanced to the last 16 with a 4-6 6-4 6-3 win.