The sixth-seeded Russian breezed through the first set before the Japanese player fought back.
Kuznetsova, who beat compatriot Elena Dementieva [ Images ] in the 2004 U.S. Open final, regained her composure to wrap up the third set.
Serbia and Montenegro's Ana Ivanovic [ Images ] also moved through with a 6-2, 6-4 win over China's Shuai Peng and will now meet second seed Amelie Mauresmo [ Images ].
Russia's [ Images ] Maria Kirilenko advanced when her Argentine opponent Gisela Dulko [ Images ] retired in the second set with an abdominal strain.
Kirilenko, who made the quarter-finals in Auckland earlier this week, was leading 6-4, 3-0 when Dulko was forced out.

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