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.
The Croats were made to pay in a big way, starting when Saul Niguez opened the scoring on 24 minutes, timing his run from deep to perfection to leap above Matej Mitrovic and thump Carvajal's cross into the bottom corner.
Croatia, so impressive in keeping the ball at the World Cup, lost confidence as Spain dominated possession and picked their opponents off easily, inflicting biggest defeat on the Croats after a 5-1 loss to England in a World Cup qualifier in 2009.
That counted as one of four assists for Asensio on the night, with a more conventional one coming four minutes after the restart when he released Rodrigo who nutmegged Kalinic for his fourth goal in six starts for his country.
La Roja got off to a slow start in the opening exchanges of the match, while Croatia seemed to have settled the better of the two teams as they surged forward easily.
Isco completed Croatia's heaviest ever defeat with a sixth before the end as Luis Enrique's youthful and exciting side produced a result which will send shockwaves around Europe. "We've played two teams that went very far in the World Cup and these victories are very important to reach the final phase, which is a challenge we have set ourselves", added Asensio. Croatia and England are both pointless after one game.
Isco capped Spain's offensive show with a right-footed shot from the center of the box in the 70th minute.
The game, contested in the southeastern Spanish city of Elche, was only Enrique's second match in charge.
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.