The 23-year-old American, ranked 108th in the world, won 6-0 6-7(3) 6-0 to move into the last 16 of a grand slam for the first time.
Czech Kvitova's loss means four of the top 10 seeds in the women's draw have failed to reach the last 16.
Rogers will face Irina Begu of Romania next after she beat Germany's Annika Beck.
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(Reporting by Martyn Herman, editing by Ed Osmond)
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