Alcaraz, aged 18, won his quarterfinal match against Berrettini with the support of Rio de Janeiro home fans. He then set up a semifinal match against Fabio Fognini, an Italian opponent.
Fognini defeated Federico Coria of Argentina 6-4, 6-2 during the quarterfinals.
Due to heavy rain in Rio this week, semifinals and quarterfinals will be played on Saturday.
Alcaraz, who also won his first professional title in Umag last year, is now ranked 29th.
Alcaraz stated, “All I can now do is to rest for two hours.”
Alcaraz and Berrettini were the final match of the rain-hit tournament’s quarterfinals. Rain interrupted the match in the afternoon, during the second set.
In the semifinals, Diego Schwartzman from Argentina and Francisco Cerundolo from Mexico will be competing.
Third-seeded Schwartzman defeated Spain’s Pablo Andujar 7-6(3), 4-6, and 6-4 on Saturday. Hours earlier, Cerundolo topped Serbia’s Miomir Kecmanovic 5-7, 6-2, 6-4.
Schwartzman stated after the nearly four-hour match that it was not clear if he would be able to play in the semifinals. He asked organizers for more time off.
“We must take care of the players.” Schwartzman stated that it would be embarrassing to enter the court in less than two hours to play a semifinal. “I don’t know if I will be able play. It will be a great match if ATP allows me to rest.