He earned repeated match points in the next game when Nadal was serving and after the Spaniard had dug deep to save three of them he could only find the net on the fourth.
But, as well as Federer and Nadal, Tsitsipas has now beaten Alexander Zverev and Dominic Thiem, both twice, and Djokovic, whom he played on hard in Canada previous year and prevailed in three sets.
He reaches the champion tournament for the 5-time.
Nadal served at 73% but that brought him nothing, facing 14 break points after barely losing a point behind the initial shot against Wawrinka last night, unable to overpower the young opponent who did everything right in sets he won.
Djokovic was handed a walkover to the last four because quarter-final opponent Marin Cilic had food poisoning and that might have explained his rusty, error-laden start as Thiem claimed an early advantage. That is because he was beaten at the semi-final stage in Monte Carlo and Barcelona, two events which he had nearly made his own over the years. "I'm very, very pleased with this win".
The Spanish second seed in Madrid had commented on the eve of his debut that he was feeling confident despite having failed to win a tournament on his favorite clay court surface so far in 2019. Don't believe? Check out the latter's reaction after nullifying a break point at 1-2 in the second set.
On the women's side, top-ranked Naomi Osaka reached the quarterfinals with a straight-set win over Aliaksandra Sasnovich and will next face Belinda Bencic, who dropped only two games in her victory over Kateryna Kozlova.
"I couldn't keep playing at the level that I wanted, but I'm very happy and very proud of my career", Ferrer said.
21-year-old Tiafoe is now the second highest ranked American player behind John Isner, but the fact that is only 37 in the world shows how far American men's tennis has fallen behind.
"I think everything went very well for me today", said Halep, a two-time champion in Madrid.