Mauresmo, the second seed, beat Italy's Silvia Farina Elia in straight sets, 6-4, 6-3. The French player takes on the winner of a match between Conchita Martinez of Spain and Nadia Petrova of Russia.
Sixth-seeded Russian Vera Zvonareva scored a three-set win over Colombian qualifier Catalina Castano 6-1, 5-7, 6-2.
Meanwhile, eighth-seeded Patty Schnyder of Switzerland reached the final eight with a straight-set victory over Ana Ivanovic of Serbia-Montenegro 6-3, 6-2.
Later, top seed and Wimbledon champion Maria Sharapova of Russia plays a third round match against former French Open winner Mary Pierce of France.
The tournament is one of several events players are using to prepare for the second major tournament of the year, the French Open, which starts May 23 in Paris.