Ramos's Real Madrid teammate Isco made it six with still 20 minutes for Croatia to endure, when he turned away from Domagoj Vida on the penalty spot and rifled a shot past the helpless Kalinic, with Asensio again the provider.
"That's why we want to win every match, but we are playing against a Spain team which didn't meet their expectations at the World Cup and are highly motivated now".
Spain can keep up their strong start following a 2-1 win over England at Wembley on Saturday as they host World Cup runners-up Croatia at Elche's Martinez Valero in Group A4, live on Sky Sports Premier League from 7.40pm.
Luis Enrique couldn't have asked for a much better start as coach of Spain's national team.
"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.
Avalancha humana en estadio de África deja 1 muerto y 37 heridos
Tal fue el error de organización que se encontraba habilitada sólo una entrada, lo que desencadenó la corrida que terminó en tragedia.
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. Saul and Asensio cut through Croatia's medium block with two precise passes, which left Rodrigo Moreno in an easy 1v1 to make it 4-0.
Saul Niguez, who is becoming an undisputable starter in Enrique's team, headed in a cross by Dani Carvajal in the 24th minute, then Marco Asensio hit two remarkable long-range shots in the 33rd and 35th to give La Roja a comfortable lead before halftime.
After this game, Croatia will host England in their next Nations League match on Friday 12 October. Sergi Roberto didn't play, so both players should be in good shape for the Real Sociedad match.
Spain were barely recognisable from the team that failed to break down Russian Federation in the last 16 but it should also be said they put six past Argentina, under Julen Lopetegui, in March. The former Barcelona coach also added defender Jose Luis Gaya and midfielder Dani Ceballos to the starting lineup.
Belgium had defeated Scotland 4-0 in a friendly last week in Glasgow.