Ferrer, seeded No. 4, converted six of 17 break-point chances, held every service game and committed only 11 unforced errors to 41 for Anderson, seeded No. 23.
When the Spaniard closed out the victory, he looked to the blue sky and raised both fists. His next opponent will be the winner of the match between two fellow Spaniards, No. 11 Nicolas Almagro or No. 32 Tommy Robredo.
Ferrer has won four matches without dropping a set. He's a four-time major semifinalist, including at Roland Garros last year.