It served Alcaraz to debut in the Masters 1000 in Rome, a tournament he had never played, to return to number 1, two months after losing the position in favor of Djokovic.
The 20-year-old Spanish phenomenon was eliminated in the Italian capital in the third round by the modest Hungarian Fabian Marozsan, coming from the classification.
Djokovic, who was defending the title in Rome, fell in the quarterfinals to the Danish Holger Rune, who lost the final to the Russian Daniil Medvedev but won a place on the list and is now sixth.
With his first win on clay, Medvedev moves up to second and sends Djokovic to third place on the ATP podium.
Beyond the Top 10 Rafael Nadal, who announced that he will not play Roland Garros and that his goal is to recover his form for one last season on the circuit in 2024, loses another place and is 15th.
The Spaniard, who had to defend his title at Roland Garros, will leave the Top-100 next month for the first time in 20 years.
Top 10 of the ATP ranking of May 22:
1. Carlos Alcaraz (ESP) 6815 pts (+1)
2. Daniil Medvedev (RUS) 6330 (+1)
3. Novak Djokovic (SRB) 5955 (-2)
4. Casper Ruud (NOR) 4915
5. Stefanos Tsitsipas (GRE) 4775
6. Holger Rune (DEN) 4375 (+1)
7. Andrey Rublev (RUS) 4270 (-1)
8. Jannik Sinner (ITA) 3435
9. Taylor Fritz (USA) 3390
10. Felix Auger-Aliassime (CAN) 3065