Zvonaryova reached the quarterfinal of the Moscow tournament, with $2,340,000 in prize money up for grabs, after easing past Agnieszka Radwanska from Poland in straight sets 6-2, 6-2.
Later in the day, Safina defeated her compatriot Anna Chakvetadze 7-6 (8-6), 6-2, and will now play for a spot in the semifinals against Zvonaryova.
Yelena Vesnina, another Russian playing on Thursday for a place in the women's singles quarterfinals, failed to reach the next round after being defeated by Nicole Vaidisova from the Czech Republic in straight sets, 3-6, 4-6.
Three Russian women, the top-seed and world No.2 Svetlana Kuznetsova, Vera Dushevina and Yelena Dementyeva, had already made it through to the last eight of the tournament.
The Kremlin Cup, held this year for the 18th time, is Russia's first-ever international professional tournament and is included in the ATP (Association of Tennis Professionals) tennis tournaments under the International Series category.
