Nadal won nine of the first 10 games in his match against fellow Spaniard Albert Montanes en route to a 6-1, 6-2 clay-court triumph at Jockey Club Brasileiro.
His quarterfinals opponent will be Portugal's Joao Sousa, who got past Spaniard Albert Ramos 7-6 (8-6), 2-6, 6-3.
Meanwhile, the third-seeded Fognini of Italy battled past Uruguay's Pablo Cuevas 7-6 (7-1), 4-6, 6-3.
Next up for him will be Alexandr Dolgopolov of Ukraine, who rallied past Argentine qualifier Facundo Bagnis 6-7 (4-7), 6-2, 7-6 (7-4).
Celebrity Families of 2014 [PHOTOS]