In his first match since changing his coaching team in an attempt to change fortunes following a hard start to the year, Djokovic was taken to three sets by Spain's Nicolas Almagro in a match which lasted for two and a quarter hours.
Nadal was also taken to three sets before seeing off Fabio Fognini 7-6 (7/3), 3-6, 6-4.
"I think he's the best clay-courter in the world, the greatest clay-courter of all-time".
"On his slump, 99 per cent of players would love to be in his position", said Nadal.
"It's been feeling good, better than I expected", Nishikori told the media in Madrid. Wednesday's match was his first since splitting with longtime coach Marian Vajda.
"I'm still finding my way to that consistency level and quality of tennis that I'm looking for", Djokovic said.
I didnt help myself find a way into the match to start playing better, said Murray. He schooled a clearly frustrated Tomas Berdych who just could not get it together when it counted, except when it came to killing his racquet at the end.
And the 12-time Grand Slam champion applied just enough pressure at the right time to break Lopez's serve in the final game of both sets.
It was the free-swinging Fognini who took the early ascendancy and had Nadal on the ropes for much of the opening set, which he even served for at 5-4 before Nadal broke back and forced a tiebreak, in which the Spaniard won the final four points to take the set.
Number one seed Andy Murray caused the biggest shock of the day as he was knocked out of the last 16 of the Mutua Madrid Open on Thursday.
This is not counting the three defeats in the finals this season, plus strong and stable tennis throughout the year in Madrid, Rafa has already won three wins, defeating Belgian Goffen 7: 6, 6: 2 without a problem in the quarter-finals.
For that Nadal-Kyrgios contest proved to be a one-sided affair, 6-3, 6-1, with the younger man undoubtedly affected by the time spent away from court in recent weeks following a family bereavement. Their first meeting was in the fourth round of Wimbledon in 2014 and a serving masterclass by Kyrgios resulted in a 7-6 (5), 5-7, 7-6 (5), 6-3 for the Australian.
He will play Croatia's world number 59 Borna Coric, who beat Pierre-Hugues Herbert of France 7-5 6-4 on Wednesday.
Djokovic now faces either Rafael Nadal or ninth-seeded David Goffin for a place in the final.
In the Women's Madrid Open, defending champion Simona Halep cruised back into the final for the third time in four years with a 6-2, 6-3 success over Latvia's Anastasija Sevastova.
A finalist in Madrid in 2014, Nishikori lost his last 10 matches against Djokovic, including in the semifinals in Madrid past year. I will check it, I hope it's not too serious. "But I can feel it a little bit".
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