Halep had eased to three consecutive wins over Magdalena Frech, Beatriz Haddad Maia and Danka Kovinic but was immediately on the back foot against Cornet in sweltering conditions during their round four contest.
Cornet fell to her knees after claiming a 6-4 3-6 6-4 victory over the two-time Grand Slam champion, and the French player has hailed her progression as a "dream come true".
"To go to my first quarter-final is just a dream come true, I don't know what to say, it is just magic," Cornet said during her on-court interview, as quoted by BBC Sport.
"I think I just stopped thinking, after 30 minutes of playing my brain was already overloaded, my vision wasn't clear any more and my hands were shaking but on the other side of the court she was not feeling much better than me.
"This is why I keep playing tennis, it's for this moment when I can share all these emotions on the court with you. The journey goes on and I can't quite believe it."
Cornet - who has reached a Grand Slam quarter-final for the very first time - now prepares to meet American Danielle Collins for a spot in the semi-finals. body check tags ::