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 20-year-old 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.
Alcaraz did not take long to put Tsitsipas under pressure, breaking him on his second service game.
The 24-year-old 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.