Second-seeded Zvonareva defeated No. 8 Alize Cornet of France 7-5, 6-1, and No. 3 Radwanska beat No. 5 Nadia Petrova of Russia 6-3, 6-2.
Zvonareva used powerful serves and groundstrokes against Cornet, who won her first WTA Tour event in Budapest, Hungary, in July.
The Russian next faces No. 5 Marion Bartoli or Alona Bondarenko in Saturday's semifinals.
Radwanska stayed on course for a fourth WTA Tour title this season by routing former champion Petrova.
The 10th-ranked Pole, who won only three games against Petrova in their previous meeting this season, took four of her opponent's service games and missed 11 more break chances.
In the semifinals, Radwanska will play either top-seeded Ana Ivanovic or Flavia Pennetta, who played later Friday.
Pablo Remaining Positive
Radwanska, Cornet reach quarterfinals in Linz
Radwanska reaches quarterfinals in Linz
Patient Pablo Waiting For Opportunities
