Top seed Sam Stosur overcame a tough challenge from France's Alize Cornet to reach the quarterfinals of the Kremlin Cup in Moscow on Thursday.

World No. 9 Stosur saved three set points in the second set before closing out the second-round match on her first match point for a 7-6(6), 7-5 victory over 43rd-ranked Cornet.

The battle lasted a minute short of two and a half hours.

The Australian now faces unseeded Czech Klara Zakopalova.

Stosur evened her head-to-head record against Cornet at 2-2 in their first meeting since 2009.

Stosur and Zakopalova have played twice, both times in Paris, with their record at 1-1.

For Stosur, this is the fifth time in six tournaments she has reached the quarterfinals, although she has only reached the semifinals twice in that time, and no finals.