"It was easier than I expected. I always expect a tough match from Jo," Federer said. "But I was able to play a clean match from start to finish and I'm really pleased."
Sixth-seeded David Ferrer withdrew before his match against Marin Cilic due to a fever.
Also advancing were ninth-seeded Nicolas Almagro and 11th-seeded Mardy Fish, while No 8 Jurgen Melzer and No 15 Viktor Troicki were eliminated.
In women's action, two-time champion Jelena Jankovic dispatched Lucie Safarova of the Czech Republic 6-0, 6-3; third-seeded Victoria Azarenka rolled past Sara Errani of Italy 6-1, 6-2; and fourth-seeded Li Na of China dispatched Lourdes Dominguez Lino of Spain 6-4, 6-2.
French Open finalist Sam Stosur also advanced, but three seeds lost: No 8 Agnieszka Radwanska, No 12 Andrea Petkovic and No 13 Ana Ivanovic.
Results from the fourth day of the ATP/WTA Italian Masters (x denotes seeding):
Men
Second Round
Roger Federer (SWI x3) bt Jo-Wilfried Tsonga (FRA) 6-4, 6-2
Feliciano Lopez (ESP) bt Philipp Kohlschreiber (GER) 6-4, 3-6, 6-3
Potito Starace (ITA) bt Viktor Troicki (SRB x15) 6-4, 6-4
Juan Ignacio Chela (ARG) bt Gilles Simon (FRA) 6-4, 6-2
Novak Djokovic (SRB x2) bt Lukasz Kubot (POL) 6-0, 6-3
Stanislas Wawrinka (SUI x14) bt Filippo Volandri (ITA) 6-1, 3-6, 6-2
Nicolas Almagro (ESP x9) bt Sam Querrey (USA) 6-3, 7-6 (7/4)
Rafael Nadal (ESP x1) bt Paolo Lorenzi (ITA) 6-7 (5/7), 6-4, 6-0
Mardy Fish (USA x11) bt Ivan Ljubicic (CRO) 7-6 (7/2), 5-7, 6-2
Florian Mayer (GER) bt Jurgen Melzer (AUT x8) 6-4 retired
Women
Second Round
Victoria Azarenka (BLR x3) bt Sara Errani (ITA) 6-1, 6-2
Yanina Wickmayer (BEL) bt Ana Ivanovic (SRB x13) 2-6, 7-6 (7/4), 6-3
Jarmila Groth (AUS) bt Bethanie Mattek-Sands (USA) 6-2, 6-4
Greta Arn (HUN) bt Alberta Brianti (ITA) 6-4, 6-4
Polona Hercog (SLO) bt Andrea Petkovic (GER x12) 6-4, 6-2
Anastasia Pavlyuchenkova (RUS x16) bt Vera Dushevina (RUS) 7-5, 6-4
Daniela Hantuchova (SVK) bt Romina Oprandi (ITA) 7-5, 6-1
Shahar Peer (ISR x10) bt Alisa Kleybanova (RUS) 6-3, 7-5
Samantha Stosur (AUS x6) bt Iveta Benesova (CZE) 6-1, 7-5
Anabel Medina Garrigues (ESP) bt Marion Bartoli (FRA x9) 6-4, 6-3
Jelena Jankovic (SRB x5) bt Lucie Safarova (CZE) 6-0, 6-3
Elena Vesnina (RUS) bt Agnieszka Radwanska (POL x8) 3-6, 6-2, 6-1
Li Na (CHN x4) bt Lourdes Domnguez (ESP) 6-4, 6-2