Alcaraz, who turns 19 on May 5, will enter the Top 10 of the ATP rankings on Monday.
He will be opposed in the next round to Australian Alex De Minaur (25th), who defeated Briton Cameron Norrie (10th) 6-3, 5-7, 6-1.
The other semi-final on Saturday will pit Argentinian Diego Schwartzman (15th) and Spaniard Pablo Carreno (19th) against each other.
In quarters, the first eliminated the Canadian Félix Auger-Aliassime (9th) 3-6, 6-2, 6-3 and the second beat the Norwegian Casper Ruud (7th) 4-6, 7-6 (10/8 ), 6-3.
Because of the rain that fell the day before, the players played their third round match on Friday before moving on to their quarter-final.
Thus, earlier in the day, Tsitsipas, seeded N.1 of the tournament, got rid of the Bulgarian Grigor Dimitrov (23rd) 6-1, 6-4 and Alcaraz, eliminated as soon as he entered the running in the Principality, had dismissed his compatriot Jaume Munar (101st) 6-3, 6-3.
© 2022 AFP