The Czech Republic's Zakopalova downed Mariana Duque-Marino of Colombia 6-4, 6-4 on the clay courts of the Jockey Club Brasileiro.
Also taking a surprise exit was fourth-seeded Romanian Alexandra Cadantu, who fell victim to Brazilian Teliana Pereira 6-3, 6-4.
Seventh-seeded Czech Barbora Zahlavova Strycova was upended as well, dropping a 2-6, 6-4, 6-3 decision to German Dinah Pfizenmaier.
Other first-round winners included South African Chanelle Scheepers, Romanian Irina-Camelia Begu, Paraguayan qualifier Veronica Cepede Royg and Austrian Patricia Mayr-Achleitner.
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