Zverev hoping to break Grand Slam duck after knocking out Alcaraz
The German third seed held off a thrilling fightback from rising Spanish star Alcaraz to win 6-4, 6-4, 4-6, 7-6 (9/7) and make the semis at Roland Garros for a second straight year.
The 25-year-old has lost three of his previous four Grand Slam last-four matches and was beaten by Dominic Thiem in the 2020 US Open final.
"I said a lot of times I'm not 21 years old anymore... I'm at the stage where I want to win," said Zverev, who has won 19 titles on the ATP Tour.
"I'm at the stage where I'm supposed to win, as well."
Zverev will face either reigning champion Novak Djokovic or Rafael Nadal on Friday for a place in the final.
"Next I have either the world number one or the 13-time champion here, so it's not getting any easier," he added.
The 19-year-old Alcaraz had been hoping to become the first teenage major winner since Nadal in Paris 17 years ago, but paid heavily for a slow start as he suffered just his second defeat on clay this season.
"He's one of the best players in the world right now," said Zverev. "I knew I'd have to be at my best from the very first point and not let him get ahead and gain confidence.
"I'm very happy to win in four sets and not have to go to a fifth."