More importantly, they are off to a winning start under Luis Enrique, with their performances in Elche and against England at Wembley a stark reminder of the quality they possess, which seemed to go missing in their tempestuous World Cup campaign.
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.
Star man Luka Modric will come up against many of his club team-mates for the visitors, and worldwide team-mate - and Barcelona player Ivan Rakitic - is happy to have the Real Madrid man on his side.
The 6-0 scoreline was Croatia's biggest-ever defeat.
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.More news: California's firefighting agency says it's running out of money
Croatia, which lost the World Cup final to France, fell apart after defender Sime Vrsaljko had to be substituted due to an injury just minutes before Spain's first goal.
The Croats were making their Nations League debut after playing European champion Portugal to a 1-1 draw in a friendly last week. Luis Enrique later added the player to the group after Diego Costa requested permission to leave the team to be present at his daughter's birth.
Asensio was one of the few changes Enrique made to the team that beat England on Saturday. They replaced Marcos Alonso, Thiago Alcantara and Iago Aspas.
Belgium striker Romelu Lukaku scored twice and won a penalty that Eden Hazard converted as they crushed Iceland 3-0 in their Nations League A, Group 2 clash in Reykjavik on Tuesday.