He had already won a penalty, scored by Sergio Ramos, as he became the youngest player to start a Nations League match.
Ramos added a header in the win.
The Real Madrid defender has now incredibly scored 10 goals in his last 15 caps.
The 34-year-old has 23 goals for his country, as many as the great Alfredo di Stefano.
Manchester City defender Eric Garcia, 19, made his debut as a second-half substitute while new City signing Ferran Torres scored a late fourth with a volley at the far post.
Fati, who was born in Guinea-Bissau but moved to Seville aged six with his family, became Spain’s youngest player in 84 years when he made his debut in last Thursday’s 1-1 draw away to Germany.
Juan Errazquin was the previous youngest scorer, against Switzerland in 1925 at the age of 18 years and 344 days.
Ethan Ampadu – who played for Wales against Bulgaria earlier on Sunday – was the previous youngest player to start a Nations League game, aged 17 years and 357 days against the Republic of Ireland in 2018.