For almost three sets Alcaraz played jaw-dropping tennis, having pulverised his opponent, who staged a brief comeback to force a tiebreak in the third.
The youngster will now face third seed Novak Djokovic in a mouth-watering semi-final on Friday with the Spaniard chasing a second Grand Slam title after winning the US Open crown last year and the Serbian veteran on course for a record-breaking 23rd men's singles major.
"This match is what everyone wanted to watch and it is going to be a really good match to play and to watch," Alcaraz said of Friday's semi-final.
"If you want to be the best you have to beat the best and he(Djokovic) is one of the best players in the world."
Alcaraz did not take long to put Tsitsipas under pressure, breaking him on his second service game.
The Greek, still searching for an elusive first Grand Slam title, could not match Alcaraz's power and precision and the Spaniard broke him to love with a sensational running forehand down the line to go 5-2 up.
He wrapped up the first set, winning 12 of the last 14 points played, but he was equally relentless in the second to break Tsitsipas in the very first game to love.
Like a bear hunting down prey, Alcaraz did not let off, forcing the Greek into the net with superb and constant drop shots or stretching him wide on his backhand.
He added another break to his rapidly growing collection to go 4-1 up and even the crowd, clearly backing Tsitsipas, could not spark a comeback as Alcaraz bagged the second set a little later with his dazed opponent double-faulting.
It was a similar story in the third as he earned a quick break and took a 5-1 lead before he squandered three match points. Tsitsipas launched a four-game comeback but Alcaraz ended it on his fifth match point.
"Of course, I lost my focus a little bit (in the third set). I was in trouble but am happy to overcome that problem and still be focused, playing a great level. But it was pretty tough at the end of the match," Alcaraz said.
"Believing in myself all the time, that's the most important thing," he said. "I always think that I am going to play these kinds of matches at this level. The key is to enjoy. That's the key," he said with his trademark beaming smile.
