Spain were three up at half-time against the World Cup runners-up thanks to Marco Asensio's two long-range strikes, the second going in off goalkeeper Lovre Kalinic, and an early header from Saul Niguez.
Asensio then laid on three more goals in the second half as Rodrigo Moreno, Sergio Ramos and Isco completed a statement victory in Elche.
Luis Enrique took charge after the humiliating exit to Russia at the World Cup had left Spain doubting the possession game that won them three consecutive major tournaments between 2008 and 2012.
He promised evolution, not revolution, and while his team still dominated possession, they were faster, more direct and less predictable in the final third.
Beating two of the World Cup's semi-finalists in four days leaves Spain top of League A's Group Two in the Nations League.
But, perhaps more importantly, it should also give the players belief in Luis Enrique's methods.
“It would be very easy to say that this is my Spain, generating many chances and conceding few goals, but the truth is that I am changing things very fast,” Luis Enrique said.
“This week everything was perfect.”
Asensio was the star of the show but Saul, so impressive against England, shone again, alongside the talented 23-year-old Dani Ceballos in midfield.
Spain were barely recognisable from the team that failed to break down Russia in the last 16 but it should also be said they put six past Argentina, under Julen Lopetegui, in March. There is work still to do.
“Comparisons with the World Cup and tonight do not make sense,” Luis Enrique said. “Today we were very effective and everything went wonderfully well. They had an early chance, they didn't take it and then we played brilliantly and scored some great goals.”
Croatia's Ivan Santini was guilty of missing early on but once Spain pulled ahead, the visitors crumbled.
Luka Modric and Ivan Rakitic, so dominant at the World Cup, never took control while defensively, without Dejan Lovren, the mistakes kept coming.
“We cannot cry about it, we have to improve,” coach Zlatko Dalic said.
“What happened has happened, all their chances have gone in and it is better that it happened today than later.
“After the first goal we were not so focused, we tried to do things too fast and started to abandon the system.
“That is not a solution against Spain, who plays well at home, who likes to dominate the ball. After the second goal, the match was over for us.”