Marco Asensio was arguably the star of the show and scored his first worldwide goal on 33 minutes by capitalising on some sloppy midfield play to collect the ball 25 yards out and beat Lovre Kalinic with a left-footed rocket.
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 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.
AP Croatia midfielder Ivan Rakitic wasn't too happy with his team's performance against Spain
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.
Aspas impressed as Spain beat England 2-1 at Wembley in League A Group 4 on Saturday.
Ten minutes later Marco Asensio made it 2-nil with a powerful shot. His second strike bounced off the post and the back of goalkeeper Lovre Kalinic, who was awarded an own goal.
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Ivan Santini and Ivan Perisic missed good early chances before Spain seized control 23 minutes in, as Saul headed the ball in off the turf after being picked out by Dani Carvajal's sublime cross. Croatia and England have no points after their respective losses to Spain.
The Croats were making their Nations League debut after playing European champion Portugal to a 1-1 draw in a friendly last week.
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.
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The first actually thing I saw related to tennis on the TV was his first or second Wimbledon championship. I was just trying to focus on myself at that time ".
Meanwhile, Zlatko Dalic offered fringe players Mateo Kovacic and Marko Pjaca opportunities to shine after their peripheral roles in their shock World Cup run.
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