And defending champion Novak Djokovic also eased into the quarterfinals with a 6-4, 7-5 win over Feliciano Lopez.
The other semi-final is between Dominic Thiem and Pablo Cuevas, and the final is on Sunday.
The Madrid Open started the rivalry, with the Caja Magica witnessing an engrossing semi-final in 2009 lasting over four hours which Nadal won after saving three match points.
Throughout their careers, the two have met have thirteen times in competitive ATP singles action.
He saved all six break opportunities he conceded to Nadal in the first set, but the fifth-ranked Spaniard took control of the tiebreaker under the closed roof on centre court. Kyrgios had 11 service winners but outside of that he struggled to make any impact with his serve, Nadal's returns were deep and accurate, taking the time of Nick's shots and neutralizing quick serve&forehand combos that Nick certainly wanted to explore.
The first set went with serve until the Serb broke his opponent to take it 6-4 but Lopez was in no mood to surrender and at 5-5 in the second he had a chance to break back at 0-30.
He will face the victor of the late night match between number 8 seed Dominic Thiem and Borna Coric, who knocked number one seed, Andy Murray out earlier in the week.
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Three times Goffin had made the semis at a Masters, and twice the quarters at a Major, but his credentials were considerable less than those of Raonic.
Kei Nishikori recovered from a terrible start to beat Argentine Diego Schwartzman 1-6, 6-0, 6-4. Of course, to be able to win 6-3, 6-1, whatever the second was, I can't remember, I think it's great news. The No 2 seed lost early at the Australian Open, Acapulco, Indian Wells, and Monte Carlo - an unusual slump in form that was followed by Djokovic parting ways with his entire coaching staff. He plays so well on the clay.
"Tomorrow I'm expecting a tough match". First played June 7, 2006, through a confrontation 26:23 in favor of Novak, who won the last 8 personal meetings with the Spaniard. I'm happy with my physically condition.
Can Djokovic come out on top?
I played really well tonight. "Obviously he didn't play very good today".
"Let's respect his level right now because it's true that perhaps it's not as high as he used to be, but I can also tell you it's (been) a lot of years".
It was ever thus for all the generations who have followed Nadal on the clay, and the chances are, it will be the same for Goffin, no matter how fast his feet.
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