Fognini, who won the Royal Guard Open in Vina del Mar, Chile, on Sunday, defeated Leonardo Mayer of Argentina 6-7 (4), 6-3, 6-2, reported Xinhua.
Robredo moved into the quarterfinals by beating Guido Pella of Argentina 4-6, 6-1, 6-4.
Fourth-seeded Nicolas Almagro, who beat Horacio Zeballos of Argentina 6-2, 7-5, advanced to the second round of the clay-court tournament.
Spaniard Pablo Andujar reached the quarterfinals upsetting Fifth-seeded Marcel Granollers 6-3, 6-0.
Eighth-seeded Jeremy Chardy of France advanced to the second round, defeating Alejandro Gonzalez of Colombia 6-4, 7-5.
Top-seeded David Ferrer plays his second-round match Thursday.
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