Third-seeded Myskina, nursing a shoulder injury, edged Frenchwoman Nathalie Dechy 4-6, 6-2, 6-1. Myskina had lost her previous two second-round matches since the Olympics and was shaky against Dechy at the beginning.
"I didn't have any self-confidence. I was nervous as usual at the start," the Russian said.
Myskina next faces countrywoman Elena Likhovtseva, who struggled past 1993 champion Mary Pierce of France 0-6, 6-4, 6-3.
"It worked out today against Dechy, but I don't know if it will be enough against the other Russians," Myskina said of her play.
Kuznetsova downed another Russian, Elena Bovina, 7-5, 6-4 and will take on Fabiola Zuluaga of Colombia, who beat Anna Smashnova-Pistolesi when the Israeli retired with a left groin strain while trailing 6-4, 1-0.
On Friday, Mauresmo meets Lisa Raymond of the United States in another quarterfinal, while second-seeded Davenport faces qualifier Jelena Jankovic of Serbia-Montenegro.
David Ferrer upset third-seeded Juan Carlos Ferrero 3-6, 7-5, 6-3 in an all-Spanish second-round match at the Lyon Open on Thursday.
Ferrer and Ferrero were both from the Valencia region but it was the first time they played each other. Ferrer will face Jonas Bjorkman of Sweden in Friday's quarterfinals.
Mikhail Youzhny of Russia, a semifinalist last year, overcame Agustin Calleri of Argentina 6-3, 6-7 (2), 7-6 (4) and claimed a last-eight berth against Xavier Malisse of Belgium.
Fourth-seeded Joachim Johansson of Sweden beat qualifier Julien Benneteau, the last remaining Frenchman, 6-3, 6-4, and will play another Swede, Robin Soderling.
Jurgen Melzer of Austria ousted Hicham Arazi of Morocco 4-6, 7-6 (4), 6-1 to advance to his seventh quarterfinals of the year, and he'll face seventh-seeded Vince Spadea of the US. It will be their fourth match this year, with Spadea leading 2-1.
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