Stephens now faces a third-round match-up against Dominika Cibulkova of Slovakia, after she bested Australia's Daria Gavrilova in straight sets, 6-3, 6-3.

World No. 3 Angelique Kerber had a fight on her hands in her second-round engagement, twice rebounding from a break behind, but managing to take out Spain's Carla Suarez Navarro in straight sets: 7-6 (4), 6-1.

The opening set saw the two aggressive players holding their own services games, and it was the Spaniard who broke first to go up two sets.

But Kerber answered with a break of her own, and the two traded breaks with Navarro serving for the set at 5-3, only to be broken by a resilient Kerber who clawed her way to deuce. Kerber broke again to level things out at 5-all, and controlled the proceedings from there despite facing a tiebreak to close out the first set.

Kerber faces the winner of tomorrow's round of 32 match between Timea Babos and China's Zhang Shuai.

World No. 8 and reigning US Open Champion Naomi Osaka of Japan had an easy 6-1, 6-0 win over Danielle Collins of the United States. Osaka was broken out of the gate by her opponent but quickly got into her rhythm, comfortably controlling the match with a solid returning effort from the baseline. Despite three double faults, Osaka fired four aces and won a stellar 89 percent of her first service points.

It was a fit way for Osaka to celebrate having just qualified for the WTA finals this year in Singapore, an announcement the association made earlier today.

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