The Chilean struck 23 forehand winners to register a 3-6, 7-5, 6-4 victory, spoiling Tsitsipas' hunt for a third successive semi-final appearance in Rome.
Djokovic, who was struck on the head by a bottle from a spectator's rucksack after defeating Corentin Moutet in his opening-round match on Friday, expressed concern about his performance against Chilean Alejandro Tabilo.
Former US Open champion Dominic Thiem on Friday announced that he will retire at the end of the 2024 season after a difficult few years owing to a wrist injury.
The former World No. 1 Andy Murray is expected to return from injury this month at the Geneva Open, indicating he will compete in the French Open the following week.