It was also the second time this year that Spain have scored six goals against World Cup runners-up, following their 6-1 win over 2014 finalists Argentina in March.
Spain's Saul Niguez celebrates after scoring his side's opening goal.
The 6-0 scoreline was Croatia's biggest-ever defeat.
Asensio takes advice from Zidane. Image PA Images
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.
Croatia started brightly as their high pressing unsettled Spain in the build-up phase, with a mishit Sergio Busquets pass leading to a shot fired wide by Ivan Rakitic. Sergio Ramos added to the scoreline with a header from Asensio's corner after some terrible marking.
He promised evolution, not revolution, and while his team still dominated possession, they were faster, more direct and less predictable in the final third.
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That proved to be the final piece of goal-mouth action as Spain claimed a second straight Nations League win.
Croatia drew 1-1 with Portugal on Thursday night in their first game since losing to France in the final in Russian Federation, while Spain will be on home soil under new boss Luis Enrique for the first time following his appointment.
Marco Asensio was on a mad one last night versus Croatia.
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The game, contested in the southeastern Spanish city of Elche, was only Enrique's second match in charge.
Enrique took over Spain after the team's elimination against Russian Federation in the round of 16 of the World Cup.
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. He was unable to cope with the pace of Asensio or Rodrigo, was pulled out of position far too often and lost Ramos at a corner for Spain's fifth.
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Luka Modric and Ivan Rakitic, so dominant at the World Cup, never took control while defensively, without Dejan Lovren, the mistakes kept coming.