It was also the second time this year that Spain have scored six goals against World Cup runners-up, following their 6-1 win over 2014 finalists Argentina in March.
The former European and World Cup winners trained on Monday ahead of the game where they will be looking to build on their ideal start after beating England 2-1 on Saturday.
Star man Luka Modric will come up against many of his club team-mates for the visitors, and worldwide team-mate - and Barcelona player Ivan Rakitic - is happy to have the Real Madrid man on his side.
Croatia will hope to get their first Nations League points when they host England next month.
Asensio, who was not among the starters against England, also set up Rodrigo's goal early in the second half with a flawless through ball behind the defence.
La Roja never looked back after Saul Niguez's headed opener.
Ten minutes later Marco Asensio made it 2-nil with a powerful shot.
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.
Croatia's biggest defeat had been a 5-1 away loss against England at Wembley in 2009.
Enrique took over Spain after the team's elimination against Russian Federation in the round of 16 of the World Cup.
Luis Enrique was thrilled with the way his side performed, including debutants Jose Gaya and Dani Ceballos, and described Asensio's shooting ability as "unique".
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.