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The third-seeded Zvonareva jumped out quickly against her Slovakian opponent in her return to the court following her straight-set loss to Serena Williams in the Wimbledon final. But the Russian was forced to scramble back after dropping the second set.
Zvonareva, ranked ninth in the world, did not appear to show any effects from the right hamstring injury that forced her to withdraw last week from the Bank of the West Classic.
Sixth-seeded Marion Bartoli of France was to face Slovakia's Daniela Hantuchova in the featured night match.
The struggles continued for former No 1-ranked Ana Ivanovic, who lost 7-6 (7/3), 6-3 to No 7 Shahar Peer of Israel. Ivanovic, the 2008 French Open champion, dropped her opening-round match for the fifth time in 11 tournaments.
Ivanovic, who got into the event as a wild card, also lost to Peer in the first round at Wimbledon. It has been nearly two years since the Serbian player won a tournament.
"I have been working so good, but it's not coming together in the matches," said Ivanovic, whose ranking has dropped to No. 60.
"I think it's just confidence. I don't really believe in my shots at that particular moment and that's what's really tough."
Yaroslava Shvedova of Kazakhstan upset Russia's Nadia Petrova 5-7, 6-4, 6-1 and fourth-seeded Agnieszka Radwanska of Poland beat South Africa's Chanelle Scheepers, 7-5, 6-3.
In other first-round matches Tuesday, No 5 Flavia Pennetta of Italy beat Ukraine's Kateryna Bondarenko, 6-2, 7-5; Russia's Maria Kirilenko defeated Kurumi Nara of Japan 6-4, 6-7 (7/4), 6-3; and wild-card Gisela Dulko of Argentina retired with a right ankle sprain while trailing American qualifier Coco Vandeweghe 6-0, 3-0.
