Twenty-four-year-old Zvonareva had no trouble dispatching Denmark's Caroline Wozniacki 6:4, 6:2 on Wednesday and will now face Belarus' Victoria Azarenko, who outplayed the 2009 Australian Open finalist 6:7, (4:7), 6:1, 6:3, to notch up her first career win against Safina.
Unseeded Anastasia Pavlyuchenkova, 17, an upcoming newcomer from Russia's Samara Region, will be hoping she can repeat Zvonareva's success when she takes on Poland's Agnieszka Radwanska, seeded seventh, in the quarterfinals later on Thursday.
In the men's tournament, Russia's Igor Andreev failed to reach the quarterfinals when he was beaten by Croatia's Ivan Ljubicic in three sets.