Women's top seed Serena Williams and defending champion Maria Sharapova also stayed on course for a potential meeting in the final as they progressed to the last four with wins over Carla Suarez Navarro and Caroline Wozniacki respectively.
Nadal has yet to win a European clay court tournament this season after defeats to Novak Djokovic at the Monte Carlo Masters and Fabio Fognini at the Barcelona Open last month.
However, he remains the heavy favourite in the Spanish capital in the absence of world number one Djokovic and will continue his quest for a fifth Madrid title against Bulgaria's Grigor Dimitrov on Friday.
"Dimitrov is a very complete player, he is one of the best in the world," said Nadal.
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"He has already won three matches here, so he is at a good level again. He played very well against Wawrinka and (Fabio) Fognini. Hopefully tomorrow I will be ready to compete well against him."
Tomas Berdych continued his impressive start to the clay court season as he also marched into the quarter-finals with a 7-5, 6-2 win over Jo-Wilfried Tsonga.
The Czech faces John Isner in the last eight after the American beat Roger Federer's conquerer Nick Kyrgios 6-3, 6-7 (7/9), 6-4.
- Williams extends unbeaten run -
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Williams extended her unbeaten record this season to 24-0 as she swept aside Spain's Navarro 6-1, 6-3.
The 19-time Grand Slam champion had to save three match points in overcoming two-time Australian Open champion Victoria Azarenka on Wednesday, but had no such trouble as she maintained her record of never having dropped a set against Navarro in their six meetings.