Djokovic had to battle from a set down to defeat Russian Karen Khachanov while Alcaraz produced a show under the lights in a 6-2 6-1 7-6 (5) victory over Stefanos Tsitsipas.
Aryna Sabalenka continued her unbeaten grand slam run by beating Elina Svitolina 6-4 6-4 to set up a last-four clash with Karolina Muchova.
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Alexander Zverev revealed last year that he was diagnosed with diabetes at the age of three. The German is unhappy that he has not been allowed to inject himself with insulin on court in Paris, telling German reporters: “They said it looks weird when I do this on court. But this is not a clever take because, if I don’t do it, my life will be in danger.”
Men: Karen Khachanov (11)
Who’s up next?
Defending champion Iga Swiatek takes on Coco Gauff in a repeat of last year’s final as the quarter-finals continue in Paris.
The winner of the clash will take on either seventh seed Ons Jabeur or Brazilian Beatriz Haddad Maia in the last four.
In the men’s draw, there is also a rematch, with Casper Ruud and Holger Rune doing battle again after their fiery encounter 12 months ago, while Alexander Zverev meets surprise package Tomas Etcheverry.