The prospective clash was immediately highlighted when the draw was made 12 days ago and had appeared inevitable as both men progressed through the rounds.
Both have dropped only one set but, while Djokovic had to fight back from a set down to beat Karen Khachanov on Tuesday, Alcaraz swatted aside fifth seed Tsitsipas 6-2 6-1 7-6 (5) in the night session.
The world number one said: “Believing in myself all the time, I’d say that’s the most important thing. I always feel I’m going to play this kind of matches at this level.
“I lost my focus a little bit at the end of the third set, I had a couple of match points. He started to play I would say better. I was in trouble but I’m really happy to overcome that problem, still playing a great level, believing that I was going to win the third set.”
Alcaraz and Djokovic have played only once before, with the Spaniard winning in Madrid last year, and he said: “This match everyone wants to watch. I would say it’s going to be a really good match to play and to watch. I really wanted to play this match. If you want to be the best you have to beat the best.”
On paper this appeared the toughest test for Alcaraz so far but he had won all four previous meetings against Tsitsipas, including in Barcelona in April, and was in total control from the start.
He was better in every aspect and Tsitsipas, who had won all six of his previous slam quarter-finals, simply had no answer to Alcaraz’s all-round wizardry, with winners flying past him and drop shots catching him out time and again.
The Greek did not play badly in the opening set but still had his serve broken twice and he appeared to grow increasingly demoralised in the second, where he won only 13 points.
The crowd were torn between admiring the flamboyant brilliance of Alcaraz and wanting a contest, and they responded to Tsitsipas’ call for encouragement when he finally won a game at 0-3 in the third set.
Alcaraz threatened to be held up more by a Mexican wave than his opponent but Tsitsipas did at least provide a late challenge, saving two match points at 2-5 and then breaking the 20-year-old for the first time when he served for victory.
A third match point came and went as Tsitsipas forced a tie-break, where he saved a fourth and fifth, but on his sixth chance Alcaraz converted.