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It was a second tour-level title for Alcaraz after his victory in Umag last year.
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.
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).
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.
Results 1-7
