Anderson broke Fish and got off to a 4-1 lead in the first set, but the American fought back and winning 5 games in a row, he took a 1-0 set lead.
Fish broke his opponent in the third game of set 2 and then once more when Anderson was serving to stay in the match.
In the last 16, Fish will play the 12th seed Spaniard Nicolas Almagro, who beat fellow compatriot Fernando Verdasco 6-3 6-4.
Also through is the 17th seed Richard Gasquet. The Frenchman dismissed Albert Ramos of Spain in three sets 6-2 5-7 6-3.
Gasquet’s next opponent will be the winner of the match between the world no.1 Djokovic and Troicki.