Four double faults in the opening set did little to help the third seed as she was broken three times before recovering to take the next two sets and seal a 2-6 6-3 6-0 win.
Sloane Stephens also progressed with a 6-3 6-3 victory over Timea Bacsinszky.
The American was rarely troubled by her opponent despite surrendering an early advantage in the first set.
"It was tough - obviously playing a player I had never played before, or even seen play, was a little bit tricky," said Stephens.
"But I thought I played pretty good overall, so I was happy to get the win."
Top seed Caroline Wozniacki progressed in far more serene circumstances, beating Mandy Minella 6-3 7-6.