Luis Enrique’s side – who beat England at Wembley in their opener in the competition on Saturday – 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.
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