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It was a second tour-level title for Alcaraz after his victory in Umag last year.
Nadal beat fellow Spaniard Pablo Carreno Busta 4-6, 7-5, 6-1, a result that gave Argentine Diego Schwartzman the last spot at the season-ending ATP Tour Finals.
The top seed was forced to save a set point before overcoming Australian Jordan Thompson 6-1, 7-6(3).
Zverev sent down nine aces and won an incredible 83 per cent of his first serve points as he cruised through the clash with 28-year-old second seed Schwartzman in 71 minutes without being broken.
Schwartzman had never beaten a top-five player at a Grand Slam and had lost his three previous quarterfinals but he produced a relentless display to set that record straight.
World number one Novak Djokovic overcame a sluggish start to lift his fifth Italian Open title on Monday, defeating Argentine Diego Schwartzman 7-5, 6-3 for a record 36th ATP Masters crown.
Schwartzman reminded Nadal that danger can lurk everywhere, even from an opponent he had beaten in all seven previous meetings and only lost two sets.