The Slovak, who won the event in 2007, is the highest-ranked player in the tournament after top-seeded Serena Williams withdrew with a foot injury. Hantuchova converted six of eight break points to set up a match with Carla Suarez Navarro.
In second-round play, Sara Errani of Italy and Andrea Petkovic of Germany both won in straight sets to advance to the quarterfinals.
Story continues below ↓advertisement | your ad hereErrani saved nine of 11 break points in defeating Czech qualifier Renata Voracova 6-2, 6-2, while Petkovic routed Britain's Anne Keothavong 6-0, 6-3.
Errani will next face fellow Italian Roberta Vinci, who eased past Sofia Arvidsson of Sweden, 6-4, 6-2.
The 36th-ranked Petkovic won the first 11 games before Keothavong, who was out for three weeks with a hip injury prior to the event, avoided a whitewash.
In first-round play, former No. 1 Ana Ivanovic beat Sorana Cirstea of Romania 6-2, 6-0. The seventh-seeded Serb entered the event on a late wild card after Williams pulled out.
The fifth-seeded Petra Kvitova of the Czech Republic beat Anastasia Rodionova after the Australian pulled out with a muscle strain in her left leg while trailing 6-2, 1-0.
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