The unseeded Mauresmo defeated sixth-seeded fellow Frenchwoman Alize Cornet 6-1, 4-6, 7-5 and unseeded Frenchwoman Aravane Rezai beat Azarenka 6-2 when the Belarusian retired after the first set with to a knee injury.
Mauresmo was last year's runner-up to recently retired Belgian star Justine Henin.
Eighth-seeded Russian Nadia Petrova beat Israeli Shahar Peer 6-2, 6-2.
Thirty-two-year-old former world No. 1 American Lindsay Davenport will play her first tennis in two months Tuesday, facing Virginie Razzano of France in a first-round match.