The world number one, looking for her first grand slam title in five years, was not at her best but was still too good for the 20-year-old Sprem as she moved into the last eight of this event for the eighth time.
Former champion Davenport raced through the first set but Sprem, a quarter-finalist at Wimbledon last year, gave herself a glimmer of hope when she broke to lead 2-0 in the second set.
However, the American raised her game to win six straight games and set up a clash with either former world number one Venus Williams or Alicia Molik, the 10th seed from Australia.
