Murray, who lost 6-7 (1/7), 6-3, 6-2 to the Frenchman, revealed that he has been carrying a back problem since December but declined to go into details on the symptoms or its treatment.\However, he did admit to facing a race against time with the French Open starting in Paris a week on Sunday.
"I've felt it for some months, but I haven't had a chance to take a pause. I've tried not to make it any worse, but the muscles get tired from compensating," said Murray, who skipped last week's Madrid Masters because of the problem.
"I've got a lot of big events coming and there's not that much time to rest any niggles. Hopefully when the French comes, the goal is to be in peak condition."
Top seed Djokovic, the defending champion, staged a 4-6, 6-2, 6-3 comeback win over Argentine Juan Monaco while second seeded Nadal was ruthless with fellow Spaniard Marcel Granollers, winning 6-1, 6-1.
"Conditions were very difficult for us. I finally settled into the match," said Nadal, who will next face Tomas Berdych after last week's Madrid finalist beat Spain's Nicolas Almagro 7-6 (7/3), 6-3.
Spanish sixth seed David Ferrer knocked out French 11th seed Gilles Simon 6-0, 7-6 (7/5).
With gusts of wind making life a challenge in all matches, Djokovic had to smash a racquet to bits to get himself motivated after losing the opening set to Monaco.
The outburst came after the Argentine had finally converted a fifth set point in the blustery conditions.
The Serb went down a break in the second set, but got it back and then broke again to level the match at a set apiece.
It took a break for 5-3 in the final set to put Djokovic into position to close out victory on his second match point.
"It was difficult to play in the wind, but it was the same for both of us," said Djokovic.
"He was able to deal with the conditions better at the start, but after a set and a half I started to play better and change my strategy.
"I never expected an easy match against him on his favourite surface. I felt I started hitting the ball better. I found my rhythm."
In the women's draw, now missing Victoria Azarenka after the world number one withdrew before her match with a right shoulder injury to hand Dominika Cibulkova a spot in the last eight, there was a win for Wimbledon champion Petra Kvitova.
The Wimbledon champion stopped Sorana Cirstea 6-2, 5-7, 6-2 while Madrid winner Serena Williams, the ninth seed, advanced over Anabel Medina Garrigues 6-3, 6-1.
Williams admitted that while she is aiming to win Rome for the first time in a decade, she is well into the countdown for Roland Garros.
"I'm getting nervous. I feel good and I've had a lot of practice on clay," she said.
"Today I was running so much, I was ready to play and feeling good. I wasn't tired at all."
Sister Venus knocked out US Open champion, and fifth seed, Samantha Stosur 6-4, 6-3.
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