The second-seeded Federer began his bid for a first title in Rome by beating Uruguay's Pablo Cuevas 7-6 (7-3), 6-4. Federer and Cuevas met in a rematch of the recent Istanbul final, which was won by the Swiss legend.
Rome is one of two ATP Masters 1000 titles still missing from Federer's collection (along with Monte-Carlo). Federer is a three-time Rome runner-up.
The third-seeded Murray improved to 10-0 on clay this year by cruising past Frenchman Jeremy Chardy 6-4, 6-3, while the fourth-seeded former world No. 1 Nadal whipped Turkish qualifier Marsel Ilhan 6-2, 6-0 at Foro Italico.
"My legs were a bit tired at the beginning," Murray said after beating Chardy. "But then I started to feel better after the first few games. For me, I felt like I played a really good match."
Chardy helped Murray's cause with 26 unforced errors.
Murray beat Nadal in last week's Madrid Masters final to capture his second clay-court title in two weeks -- the first two clay titles of his career.
Meanwhile, fifth-seeded U.S. Open runner-up Kei Nishikori handled Czech Jiri Vesely 7-6 (7-3), 7-5.
Upsets came when Italy's own Fabio Fognini toppled 10th-seeded Bulgarian Grigor Dimitrov 7-6 (11-9), 4-6, 6-0, Serbian Viktor Troicki outlasted 11th- seeded Spaniard Feliciano Lopez 6-7 (2-7), 6-4, 6-3, Austrian Dominic Thiem tackled 12th-seeded Frenchman Gilles Simon 7-6 (7-5), 2-0, retired, David Goffin of Belgium defeated 13th-seeded Frenchman Jo-Wilfried Tsonga 6-2, 4-6, 7-5, and Brazilian qualifier Thomaz Bellucci overcame 14th-seeded Spaniard Roberto Bautista Agut 1-6, 6-1, 6-4. Bellucci will meet the current world No. 1 and reigning Rome champ Djokovic on Thursday.
Also on Day 3, 16th-seeded American John Isner topped Argentine Leonardo Mayer 7-6 (8-6), 6-4 and Spaniard Guillermo Garcia-Lopez dismissed Ukrainian qualifier Alexandr Dolgopolov 6-4, 6-3. Isner is rewarded with a third-round match against the clay-court wizard Nadal.