France's top seed spoilt home country hopes with her elimination of Sun Tiantian 6-3, 6-2 on Thursday in the second round.
But seventh seed Li Na saved face with a comeback win over Russian Elena Vesnina 3-6, 6-1, 6-1 to move into a match with second seed Svetlana Kusnetsova.
Davenport, who won the last of her three majors in 2000, beat China's Zheng Jie 6-2, 7-6 (7-4).
For the second straight match, the 30-year-old American struggled, sweeping the opening set but losing an early break in the second before pulling out the win in one hour, 23 minutes despite losing serve three times.
Zheng, ranked 33 and winner of titles in Estoril and Stockholm this season, was unable to take it into a third set as Davenport collected victory in a tiebreaker.
Mauresmo has lost a dozen times to Davenport, her last win in the 2000 Sydney final.
Mauresmo earned the first set against the 111th-ranked Chinese, the 2004 Athens Olympic doubles gold medallist, in 36 minutes, recovering after losing an early break of serve.
But the top seed wasted no time in consolidating, collecting a break to start the second set and reaching a 5-1 lead against Beijing player.
Sun saved one match point before Mauremso advanced with four breaks of serve and five aces in her efficient debut at the event.
Serbian sixth seed Jelena Jankovic beat out France's Marion Bartoli, 6-3, 6-2.
Russian third seed Nadia Petrova moved into a quarter-final matchup with Jankovic as she crushed Greek Eleni Daniilidou 6-1, 6-2 in 67 minutes, firing ten aces while saving all eight break points she faced.
Results:
Second round: 7-Na Li (China) beat Elena Vesnina (Russia) 3-6, 6-1, 6-1; 5-Lindsay Davenport (U.S.) beat Jie Zheng (China) 6-2, 7-6 (7-4); 3-Nadia Petrova (Russia) beat Eleni Daniilidou (Greece) 6-1, 6-2; 1-Amelie Mauresmo (France) beat Tiantian Sun (China) 6-3, 6-2; 6-Jelena Jankovic (Serbia) beat Marion Bartoli (France) 6-3 ,6-2.—Agencies