The fifth seed reached his 10th straight grand slam last eight by beating the 2.03 metre (6ft 8in) South African, who towers nearly 30 cm (1 ft) above him.
Ferrer dominated baseline rallies with the 19th seed in the first two sets before they exchanged breaks in the third and Anderson worked the angles better, sending Ferrer scampering and sliding and taking the tiebreak when the 32-year-old put a forehand into the net.
Ferrer fought straight back in the fourth, unleashing a string of forehand winners to break Anderson in the second and fourth games to win the match.
Watch all the action from the French Open on up to seven courts on the Eurosport Player.
Results from the French Open men's singles matches on Monday
1-Rafa Nadal (Spain) beat Dusan Lajovic (Serbia) 6-1 6-2 6-1
5-David Ferrer (Spain) beat 19-Kevin Anderson (South Africa) 6-3 6-3 6-7(5) 6-1
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