Backed by a partisan Spanish crowd, Nadal on Friday dispatched the Swiss veteran in just an hour and eight minutes, and will move on to the last four of the competition, where he will face Greece's Stefanos Tsitsipas, Efe news reported.
Wawrinka came into this quarter-final in fine form, having not lost a set or a service game in three matches this week against France's Pierres-Hugues Herbert, Argentina's Guido Pella and Japan's Kei Nishikori.
But the three-time Grand Slam champion had no answer for Nadal's energy and mobility, as the Spaniard pushed him around the court to force the 34-year-old into multiple errors.
The Spanish world number two hit 72 per cent on his first serve and did not concede a single break point while breaking Wawrinka's four times on route to his 70th appearance in a Masters 1,000 semi-final, and his 11th in Madrid.
"A very positive match, I'm very happy with the way I played and in general terms, it was a great performance. I'm really happy to get through (to the semis) in this way", Nadal said after the game.
He said he would use his performance against Wawrinka as "an example" for how to approach his next challenge against the Greek rising star.
"He's playing last week, he will come to the semi final with a lot of confidence".
That win was his seventh in a row since last week, where he won his second title of the season in Estoril, Portugal.
Nadal will be taking on Tsitsipas for the fourth time; their most recent match-up came at this year's Australian Open, when Nadal beat the 20 year-old.
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