Federer won through 6-4, 6-3 against the 72nd-ranked Sousa and will play Croatian 13th seed Borna Coric later in the day for a place in the quarter-finals after rain delays wiped out play on Wednesday.
Federer, a four-time finalist in Rome, returns to Italy after skipping the clay season for the last two years as he concentrated on his grass game.
Latest results from the ATP and WTA Italian Open tournaments in Rome on Thursday (x denotes seeding):
Naomi Osaka (JPN x1) bt Dominika Cibulkova (SVK) 6-3, 6-3
Mihaela Buzarnescu (ROM) bt Julia Goerges (GER x16) 6-4, 3-6, 4-4 retired
Carla Suarez (ESP) bt Alize Cornet (FRA) 6-3, 3-0 abandon
Kiki Bertens (NED x6) bt Amanda Anisimova (USA) 6-2, 4-6, 7-5
Johanna Konta (GBR) bt Sloane Stephens (USA x7) 6-7 (3/7), 6-4, 6-1
Garbine Muguruza (ESP) bt Danielle Collins (USA) 6-4, 4-6, 6-2
Kristina Mladenovic (FRA) bt Belinda Bencic (SUI) 6-2, 2-6, 6-1
Diego Schwartzman (ARG) bt Albert Ramos (ESP) 7-6 (7/5), 6-1
Jan-Lennard Struff (GER) bt Marin Cilic (CRO x9) 6-2, 6-3
Kei Nishikori (JPN x6) bt Taylor Fritz (USA) 6-2, 6-4
Roger Federer (SUI x3) bt Joao Sousa (POR) 6-4, 6-3
Fernando Verdasco (ESP) bt Dominic Thiem (AUT x5) 4-6, 6-4, 7-5
Rafael Nadal (ESP x2) bt Jeremy Chardy (FRA) 6-0, 6-1