Rafael Nadal edges Andy Murray
Murray jumped out to a 5-0 lead and won the first set in just 37 minutes with a dominant display, as the Wimbledon champion unleashed a series of winners from just about everywhere on the court.
But the top-ranked Nadal broke early in the second set and took control with a late break in the third to stay on course for his eighth title in Rome.
"I really didn't feel like I was playing bad in the first set. Probably tactically (it was) not good but inside the energy was really good," Nadal said. "Tonight I didn't have any negative thoughts for the whole match. ... I closed the match at the first opportunity."
There were a series of breaks early in the third set and Murray took a 4-2 lead. But the British player was upset with the way he played the next game.
"That was my chance there and I played a poor game so I'm disappointed with that," Murray said. "I maybe rushed a little bit, because I was being very patient for the majority of the match. ... Physically, he was a little bit stronger at the end."
It was the third consecutive match in which Nadal was pushed to three sets, leaving his clay-court form in question entering Roland Garros, which starts in nine days.
"The physical part is really good, the mental part, too, and my tennis is going to be there sooner or later," Nadal said. "This was one of my best matches in a while."
And despite losing in the end, it was a positive performance for Murray, who is still trying to regain his top form following minor back surgery in September.
"I'm getting close to getting back to where I want to be, and that's pleasing with a couple of big months ahead," Murray said. "Tonight was probably the best I've hit the ball for a while, and the best I've felt physically since the surgery."
Djokovic is back on track after a right wrist injury sidelined him last week. And Serena Williams is cruising again, too, after being slowed by a left thigh problem.
The second-ranked Djokovic overcame a stiff challenge from David Ferrer before grinding out a 7-5, 4-6, 6-3 win and the top-ranked Williams then rolled past Zhang Shuai of China 6-1, 6-3 to stay on course in her title defense.
Williams' semifinal opponent will be 2008 French Open champion Ana Ivanovic, who beat 13th-seeded Carla Suarez Navarro 6-4, 3-6, 6-4.
Errani took advantage of a supportive crowd to beat second-seeded Li Na 6-3, 4-6, 6-2 and reach the semifinals for the second consecutive year, while Jankovic eliminated third-seeded Agnieszka Radwanska 6-4, 6-4.
Dimitrov celebrated his 23rd birthday with a win when 36-year-old Tommy Haas retired after losing the first set 6-2 due to a right shoulder injury -- spoiling a matchup between the youngest and oldest players in the top 20.
The big-serving Raonic held off Jeremy Chardy of France 6-3, 5-7, 6-2 on an overcast day with intermittent rain at the Foro Italico.
Djokovic double-faulted on his first match point but then won a 38-shot rally before eventually closing it out in just over 2½ hours.
"It was definitely the most physical match I've had on clay this year," Djokovic said, adding that his wrist is reacting well. "I'm playing with no pain. As long as it stays like this I'll be happy."
The 10th-seeded Errani is attempting to become the first Italian to win the tournament since Raffaella Reggi took the title 29 years ago in Taranto.
The last Italian man to win was Adriano Panatta back in 1976.
Li had won all six previous meetings with Errani but she was unusually inconsistent this time, committing 52 unforced errors to Errani's 21, and appeared rattled by a close call from the chair umpire early in the third set.
Errani celebrated by waving her arms to incite the crowd.
"I did well not to get carried away by the euphoria," Errani said. "It's difficult to describe how it felt at the end. The fans were incredible."