Mauresmo, the 2006 Wimbledon and Australian Open champion, dominated the opening set of the first-round match with some impressive backhand volleys and a succession of errors from Cornet.
But the 18-year old Cornet settled down in the second set. With Mauresmo struggling to put the ball away in many rallies, Cornet broke to lead 4-3.
Mauresmo had to fight off two break points at the beginning of the third set, but broke for the match when Cornet sent the ball long.
"The way I played in the first set was great,'' Mauresmo said. "I didn't keep that level up. I started to play a little bit more from the baseline and not being as aggressive as I was at the beginning. That put her back into the match and things got a little bit more even.''
In other first-round matches, fifth-seeded Victoria Azarenka retired with a left knee injury after losing the opening set 6-2 against Aravane Rezai. Also, eighth-seeded Nadia Petrova defeated Shahar Peer 6-2, 6-2, Gisela Dulko beat Tathiana Garbin 3-6, 6-4, 6-2, Samantha Stosur ousted Katie O'Brien 6-4, 6-3 and Li Na overcame Casey Dellacqua 6-2, 6-4.
Svetlana Kuznetsova, Marion Bartoli, Vera Zvonareva and Agnieszka Radwanska all have a bye into the second round.
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