Nadal showed no signs of the fever that had brought him to the brink of pulling out on Thursday in a typically clinical display, hammering the World number 23 to set up a semifinal against Richard Gasquet or Tomas Berdych.
Champion for five of the past six years, Nadal raced into a 4-0 lead, breaking Cilic's serve with a ferocious forehand topspinner and backhand crosscourt shot before taking the first set in the Italian sunshine.
The Croat stayed with the Spaniard until the seventh game of the second set when the top seed moved up an extra gear to break twice more, bringing his overall win-loss run in Rome to 30-1 and raising the prospect of another mouthwatering final against Novak Djokovic.
The win meant the Serb now has no chance of overhauling Nadal at the top of the rankings before the French Open starts in just over a week. World number four Murray earlier became the first British player in the tournament's professional era to reach the final four after coming back from a set down to defeat unseeded German Florian Mayer 1-6, 6-1, 6-1.
The Scot opened the match in ragged fashion by dropping the first set before storming to victory to book a semifinal against Djokovic, his conqueror in January's Australian Open final, or fifth seed Robin Soderling.
"It's nice to do well here but now I want to go further," Murray, who in six previous visits had never got beyond the third round, told reporters. "It will be great to play Novak. He's playing really well though I haven't seen him play this week. I won't be able to get away with playing the way I did in the first set."
Federer stunned
Roger Federer failed to make the quarterfinals of a tournament for the first time in a year on Thursday while Rafael Nadal returned to form in the third round despite almost withdrawing with a fever.
Novak Djokovic then stretched his unbeaten run for the year to 34 matches after winning eight of the last nine games against Swiss Stanislas Wawrinka to triumph 6-4, 6-1.
Third-seed Federer took the first set 6-4 against France's Richard Gasquet but, in a match of clean-hitting strokes, lost the next two sets against the 16th seed on tiebreaks.
Gasquet won 4-6, 7-6 (7-2), 7-6 (7-4).
The Swiss, who had won the last eight matches between the two, broke serve in the very first game but Gasquet responded with 10 straight points to draw level at 2-2.
The long thrilling rallies had both players covering every bit of the court but it was Federer who broke again in the seventh game with two sweet forehands to take the set.
Gasquet, whose one victory against Federer had come on clay at Monte Carlo in 2005, fought back by trouncing the tired-looking Swiss in the second set tieback with a backhand winner before a flourishing crosscourt forehand. With games going with serve in the deciding set, Gasquet again showed a steelier side, forcing Federer into two top-spin backhand errors in another confident tiebreak to take the scalp.
Meanwhile, Francesca Schiavone set up a repeat of last year's French Open final against Samantha Stosur in the women’s quarterfinals as top seed Caroline Wozniacki also advanced to the last eight on Thursday.
Dane Wozniacki dispatched Belgian Yanina Wickmayer 6-1, 7-6 after Schiavone took advantage of rowdy home backing to recover from a set down to defeat Slovak Daniela Hantuchova 3-6, 6-2, 7-5.
