Stosur, who won this tournament in 2009, hit five aces and converted five of six breakpoint chances to win in 1 hour, 16 minutes at Utsubo Tennis Center.
Jamie Hampton of the United States overpowered Japan's Ayumi Morita 6-3, 6-2 while France's Pauline Parmentier beat compatriot Mathilde Johansson 6-2, 6-2 to also advance.
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