Hantuchova prevailed 6-3, 7-6 (8-6) to set up a second-round meeting with Kaia Kanepi.
Anastasia Pavlyuchenkova, the No. 3 seed, made it to the quarterfinals with a 6-2, 6-3 victory over Polona Hercog.
The day's biggest upset came when Alize Cornet surprised No. 7 seed Aleksandra Wozniak 6-2, 6-3.
Other second-round winners included Vania King and Klara Zakopalova.
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