Dementieva, into the last eight for the third time in her career, suffered her trademark service jitters, hitting seven double faults, but Scheepers did not have the arsenal to upset the Russian's rhythm.
Scheepers, the first South African to reach the fourth round here for 13 years after also playing three matches in qualifying, never mastered the breezy conditions on Court Philippe Chatrier and limped out after an hour and 14 minutes. Dementieva will face second seed Venus Williams of the US or Russian 19th seed Nadia Petrova for a place in the semi-finals.