Cuevas will face Dominic Thiem in the semi-finals after the Austrian brushed aside Andy Murray's conqueror Borna Coric in a one-sided last eight clash.
Novak Djokovic staved off a huge upset in his first match since splitting with his long-time coaching team to beat Nicolas Almagro 6-1, 4-6, 7-5 in the second round of the Madrid Masters on Wednesday.
His next match against the 22-year-old No16 seed Nick Kyrgios was highly anticipated, a genuine contender for the "popcorn" match of the day.
"Most things weren't working particularly well". He only made it to the main draw after Richard Gasquet withdrew because of a back injury. "It's going to mean to me a lot", Coric said. Djokovic won 6-1, 4-6 and 7-5.
Nishikori, a finalist in Madrid in 2014, is playing in his first tournament since March.
Spaniard Almagro, who has never gone beyond the quarter-finals in a grand slam, grew in confidence in the second set, however, with the backing of the home support and saved two break points before forcing a decider.
The victory was the Canadian's second win in four matches against the 26th-ranked Muller.
The point here-as with all previous scrutiny of the Serb-is not to demean the players beaten by Djokovic, but to call attention to how precipitously one of the sport's all-time greats has declined.
"I haven't played bad, I played really bad", Nadal said.
"I'm sure the discussions about whether to give it or not were long. but they've obviously done what they think is right for that event and maybe haven't thought as much about the wider implications".
On the other hand, Djokovic has not had the best of starts to the season as he is yet to reach the final of a tournament after his title-winning run at Doha. "My physical condition is also getting better", said Nishikori, who is now 9-4 in his career meetings with Ferrer. This is the brand of emphatic shot-making that kept him in the match: a tightly angled return to yank Djokovic off the court, then seizing the ball early and beating it down the line, hard but with a healthy margin for error.
Nadal was also taken to three sets before seeing off Fabio Fognini 7-6 (7/3), 3-6, 6-4.
Defending champion Djokovic will play the victor of Rafael Nadal and David Goffin in Saturday's last four.
The quarter-finals of the women's tournament saw Simone Halep, the highest surviving seed, breeze past American Coco Vandeweghe 6-1, 6-1, while 14 seed, Kristina Mladenovic defeated Sorana Cirstea 6-4, 6-4 and unseeded Latvian Anastasija Sevastova had a straight-set triumph 6-3, 6-3 against Kiki Bertens. "I don't want to put burden on my wrist". "It's always tough to play with someone who has a big serve".