Alcaraz, playing on the same Court Philippe Chatrier at Roland Garros where he captured the French Open in June, saw off 13th-ranked Tommy Paul of the United States 6-3, 7-6 (9/7).
The 21-year-old Alcaraz recovered from a break down in the second set to defeat Paul, having also beaten the American in the quarter-finals at Wimbledon on his way to the title at the All England Club last month.
In the second set tie-break, when he had to save a set point, the tension was too much even for Queen Letizia, who cut a nervous figure courtside before joining in a rousing standing ovation for her crowd-pleasing compatriot.
"It's all about the fight," said Alcaraz, who was playing the day after he and Rafael Nadal suffered a heartbreaking doubles loss in what was probably the veteran's final appearance at Roland Garros.
"Maybe I was a little tired from all the emotion of yesterday, playing with Rafa but I gave it everything on court," said Alcaraz.
"I had to play with intensity because Tommy is such a great athlete. I was a bit tired at the end but I just remember that I am playing for my country as well as myself."
The Spanish star will face either Casper Ruud or Felix Auger-Aliassime for a place in the gold medal match.
Top seed Djokovic, in the other half of the draw, tackles Stefanos Tsitsipas in his quarter-final later Thursday.
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