La Roja dominated the match after Saul Niguez started the scoring with an expert header off a cross from Dani Carvakhal in the 24th minute.
Asensio, who was not among the starters against England, also set up Rodrigo's goal early in the second half with a ideal through ball behind the defence.
It got worse for Croatia before the break as Asensio grabbed two memorable goals in the space of two minutes, first blasting beyond Kalinic from 25 yards before driving towards the box and curling a stunning effort that smacked the crossbar and went in off the unfortunate goalkeeper.
Three goals in the space of 11 first-half minutes put the hosts on their way to a second successive UEFA Nations League victory, and they were five up before the hour mark.
"We've played against teams who got very far in the World Cup". And finally, a memorable result was capped by a final goal by Isco.
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"Croatia are the World Cup runners-up and all teams will be motivated against us - and we have to be aware of that". To reach the Nations League finals next June, Spain need just two points from their remaining two games, at home to England and away to Croatia.
Spain have rattled in the goals against Croatia to take charge of their Nations League group.
Ivan Rakitic, winning a 100th cap that he will want to forget, eventually ran onto a stray back-pass from Sergio Busquets but could not get enough bend on his first-time shot to sneak it inside David de Gea's post.
Rodrigo - who scored the victor 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.
Spain's next match takes place in exactly a month, when they visit Cardiff for a friendly match four days before hosting England in the Nations League.