The first five games of the opening set went with serve, which meant that world number five Ferrer led 3-2.
He then claimed a break of his South African opponent's serve to go 4-2 in front, before holding his next two service games to go one set in front.
Anderson's response to falling behind was initially positive, with both players holding their first two service games each.
However, Ferrer then took control and went on to win four games in succession, which resulted in him opening up a two-set lead.
The third set was evenly contested throughout as both players failed to claim a break of the other's serve. Anderson had the best chance when, leading 5-4, he passed up three break points that would have given him the set.
That missed opportunity eventually resulted in a tie-break, which Ferrer took control of from the outset. Having lost the first point, 30-year-old Ferrer won seven of the next nine to secure his place in the next round.