Ivanovic downed Sybille Bammer of Austria 6-4, 6-2 in a second-round match, while Zvonareva routed Nuria Llagostera Vives of Spain 6-2, 6-0.
Ivanovic dropped serve twice in the opening set before settling after breaking Bammer for a third time at 4-4.
"I am happy with the way I played and beating her in straight sets is a good result,'' said Ivanovic, who improved to 2-1 against Bammer. "During the first set, I realized I had to take the ball earlier so I could put more pressure on her. That made things easier for me.''
Ivanovic will play seventh-seeded Flavia Pennetta of Italy, who defeated Dominika Cibulkova of Slovakia 6-3, 6-1. Pennetta reached the final of the Zurich Open last week.
Zvonareva dropped serve in the opening set against Llagostera Vives and saved five more breakpoints, but was in control afterward.
The Russian is next up against No. 8 Alize Cornet.
Fifth-seeded Nadia Petrova defeated Katarina Srebotnik of Slovenia 6-4, 7-6 (7) to set up a quarterfinal match against No. 3 Agnieszka Radwanska.
Petrova, who won the tournament in 2005, was broken twice while serving for the match at 5-4 and 6-5, and the Russian missed four match points in the tiebreaker before finally converting.
Alona Bondarenko of Ukraine was the only unseeded player to make the quarterfinals by beating fourth-seeded Patty Schnyder of Switzerland 6-2, 2-6, 6-1.
Bondarenko lost only three points on serve in the opening set, but had many errors from the baseline in the second.
Schnyder, who reached the final last year, didn't win a service game in the decider.
Bondarenko's next opponent was sixth-seeded Marion Bartoli of France, who beat Petra Kvitova of the Czech Republic 7-6 (4), 1-6, 6-3.
Petrova, Bartoli advance at Generali Ladies
Radwanska, Cornet reach quarterfinals in Linz
Agüero: I Was Inspired
