For whatever it's worth, the revamped Spain team looked quite sharp, using a more direct approach than the various forms of tiki-taka we have come to expect since La Roja's 2010 World Cup win.
Spain were in dreamland two minutes later as Asensio cheekily lofted a shot from 20 yards that ricocheted off the crossbar, before deflecting in off goalkeeper Lovre Kalinic for the third goal.
The Croats were made to pay in a big way, starting when Saul Niguez opened the scoring on 24 minutes, timing his run from deep to perfection to leap above Matej Mitrovic and thump Carvajal's cross into the bottom corner.
Rodrigo scored after slipping past the Croatian backline on a through-ball from Asensio in the 49th minute.
Luis Enrique's charges got their campaign underway over the weekend with a 2-1 win over England at Wembley Stadium.
"It's a great challenge to play against Luka in the Spanish league and it's even better to play with him for our country", Rakitic said. To reach the Nations League finals next June, Spain need just two points from their remaining two games, at home to England and away to Croatia.
Isco capped Spain's offensive show with a right-footed shot from the center of the box in the 70th minute.
Luis Enrique couldn't have asked for a much better start as coach of Spain's national team. Three superbly weighted deliveries of different styles gifted his side further goals in the second half and underlined his remarkable quality.
The centre-back was consistently excellent in Russian Federation but was given a torrid time here.
Sergio Ramos, one of the remaining members of Spain's golden generation, added the fifth goal with a header off a corner kick in the 57th minute, and Isco closed the scoring in the 70th after another set up by Asensio. This will be the team's first Nations League match.