The former world No. 1 Federer got past 15th-seeded South African Kevin Anderson 6-3, 7-5, while the fourth-seeded former top-ranked Nadal handled 16th-seeded American John Isner 6-4, 6-4 on Thursday at Foro Italico.
Federer is a three-time runner-up in Rome, including 2006 and 2013 versus his great rival Nadal.
The nine-time French Open champion Nadal was last year's Rome runner-up to three-time champ Novak Djokovic. The two great stars have combined to win the last 10 titles at this Masters 1000 tournament.
Nadal will face Swiss slugger Stan Wawrinka in Friday's quarterfinals.
Meanwhile, Murray said he was fatigued after winning each of the last two clay-court events in Munich and Madrid.
"It's been a very long three weeks for me, the longest I've ever had on clay," said Murray, who had never even reached a clay-court final before his triumph in Munich.
Murray followed that with a surprising win in Madrid, beating Nadal in the final.
"The point is I did not expect to do what I have done in the past few weeks," Murray added. "My body has never done that before on clay. My body's always found the surface difficult. I also don't want to risk making it worse. In the past maybe I've done too much."
"I wanted to play in this tournament, it's a big event with a lot of points on offer," Murray continued. "The time of year is tough for everyone, it's just one of those things."
David Goffin of Belgium earned a spot in the quarterfinals with the walkover against Murray, who's still 10-0 on clay this year.