Bartoli will next face defending champion Francesca Schiavone, who rallied to beat Anastasia Pavlyuchenkova 1-6, 7-5, 7-5.
The 11th-seeded Frenchwoman overcame a 3-1 deficit in the tiebreaker to take a first set in which Kuznetsova had five double-faults and both players combined to drop serve six times.
The victory was the 400th of the 26-year-old Bartoli's career.
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