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.
Croatia suffered the biggest defeat in their history as Spain thrashed them 6-0 in Tuesday's Nations League match at Estadio Manuel Martinez Valero.
Croatia's Ivan Santini was guilty of missing early on but once Spain pulled ahead, the visitors crumbled.
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.
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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.
The 48-year-old head coach included six Real Madrid players in the starting lineup - including Man of the Match Marco Asensio who was directly involved in five of Spain's six goals - but only Sergio Busquets was included from Enrique's former club.
Playing in a small venue in Elche - a site that rarely gets to host Spanish national team games - should confer the hosts a more significant, more intimidating home-field advantage than the usual atmosphere of a pseudo-friendly game played in the larger, cavern-like stadiums.
Croatia will hope to get their first Nations League points when they host England next month. "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. But Spain weren't finished, 8 minutes later, Serjio Ramos scored the 5th from a corner kick.
Croatia meet the Three Lions in a repeat of the World Cup semi-final on October 12 in Rijeka.