Luis Enrique’s side – who beat England at Wembley in their opener in the competition on Saturday (September 8)- never looked back after Saul Niguez’s headed opener.
Marco Asensio fired in from 20 yards and then, shortly after, saw another rifled effort hit the bar and find the net via Croatia keeper Lovre Kalinic.
Rodrigo, Sergio Ramos and Isco made it a rout for the superb Spanish.
Rodrigo – who scored the winner at Wembley – beat the offside trap before finishing neatly, Ramos headed in from a corner and Isco turned sharply before firing in from inside the box.
Croatia, whose side contained just four of those who started the World Cup final in Moscow this July – defender Domagoj Vida and midfielders Luka Modric, Ivan Rakitic and Ivan Perisic – had actually started the game the stronger but now have to regroup before facing England in October.
Spain’s two wins out of two in the Nations League see them top League A Group 4 with 6 points. Croatia and England are both pointless after one game.