Ranked 96th but holding a 3-0 head-to-head record against her higher-ranked opponent, the big-serving Shvedova -- making her 10th appearance at Wimbledon -- powered down seven aces and hit the mark with three quarters of her first serves.
Another serve proved decisive on the final point when Safarova hit her return long.
Shvedova faces the winner of the match between American veteran Venus Williams and Carla Suarez Navarro of Spain.
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(Reporting by John Stonestreet, editing by Ed Osmond)
