Zlatko Dalic's men were happy to sit back at times, though, and the first goal came from an accurate switch of play by Sergio Ramos to Dani Carvajal who crossed for Saul Niguez to head home. Rodrigo Moreno completed a fine team move after the interval before captain Sergio Ramos headed the fifth while a strike from Isco saw Spain become the first team to score six against Croatia as they charged top of League A, Group 4 on six points.
Croatia, whose side contained just four of those who started the World Cup final in Moscow this July - defender Domagoj Vida and midfielders Luka Modric, Ivan Rakitic and Ivan Perisic - had actually started the game the stronger but now have to regroup before facing England in October. "They had an early chance, they didn't take it and then we played brilliantly and scored some great goals".
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.
It got worse for Croatia before the break as Asensio grabbed two memorable goals in the space of two minutes, first blasting beyond Kalinic from 25 yards before driving towards the box and curling a stunning effort that smacked the crossbar and went in off the unfortunate goalkeeper. Bustling forward Lukaku was bundled over by Sverrir Ingi Ingason in the 28th minute and the referee immediately pointed to the spot, with Chelsea playmaker Hazard calmly sending Hannes Halldorsson the wrong way with the resulting penalty.
In other Uefa Nations League games, England edged Switzerland 1-0, Belgium beat Iceland 3-0, and Poland and Ireland played out a 1-1 draw.
Ten minutes later Marco Asensio made it 2-nil with a powerful shot. Yet despite missing one of their main playmakers, there was no lack of creativity in the side.