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.
The World No. 4 Daniil Medvedev, who has been one of the most consistent performers on the ATP Tour across the past five years, registered a triumph over Alexander Bublik at the Madrid Open to reach the quarter-finals on Tuesday
The Italian may have never advanced past the third round at the Caja Magica, but Alcaraz believes it won't matter to a player who has a 25-2 start to the year
Pitted against world No. 7 Holger Rune in the second round, Sumit Nagal gave the Dane, placed 86 places above him in the rankings, a run for his money before succumbing to a 3-6, 6-3, 2-6 loss