Croatia's best moment came before the first whistle even blew.
Then Rodrigo headed Carvajal's cross early in the 2nd half to make it 4-nil.
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.
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. "We needed to recuperate the feelings we had before, we've played two great games", said goalscorer Asensio, who also provided three assists. We played two big games, our fans supported us, and it's nice to play here.
Spain's two wins out of two in the Nations League see them top League A Group 4 with six points.
Spain coach Luis Enrique has admitted he made a mistake to not select Celta Vigo forward Iago Aspas in his initial squad after seeing him in training.
The two nations are facing each other for the seventh time, with Croatia taking the last meeting - a 2-1 win at Euro 2016.
The hosts will need to be in better form against Romelu Lukaku and Eden Hazard than in their last game, the first without influential manager Heimir Hallgromsson, where they were beaten 6-0 by Switzerland.
Spain opened up their Nations League A campaign with an impressive 2-1 comeback victory over England over the weekend - while Croatia laboured to a 1-1 draw with European champions Portugal in a friendly fixture.
Ten minutes later Marco Asensio made it 2-nil with a powerful shot.
With victories over England and Croatia this global break under new manager Luis Enrique, Asensio thinks they have recaptured some of the good vibes they felt before the World Cup.