Midfielder Saul Niguez scored in his home city of Elche by heading home midway through the first half, giving Spain the lead against the run of play after Croatia had made a bright start and missed two good chances.
The hosts soon increased their lead with two thumping strikes from Marco Asensio, the second of which was given as an own goal to Croatia goalkeeper Lovre Kalinic as it bounced off him after crashing against the crossbar.
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.
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. Spain were in a confident mood after winning their first game under Luis Enrique 2-1 away to England in their Nations League opener on Saturday and once they scored the floodgates opened and Croatia were left chasing shadows.
"We played a spectacular game and rounded off a brilliant week. We needed to recuperate the feelings we had before, we've played two great games," said goalscorer Asensio, who also provided three assists.
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.
"We've played two teams that went very far in the World Cup and these victories are very important to reach the final phase, which is a challenge we have set ourselves," added Asensio.
Rashford gets England back to winning ways
England bounced back from three consecutive defeats for the first time in 30 years as a much-changed side edged past Switzerland for a 1-0 friendly win in Leicester thanks to Marcus Rashford's winner.
The Three Lions failed to hit the heights from their World Cup campaign in a laboured performance against an impressive young Swiss outfit.
However, Gareth Southgate did at least stave off an unwanted record of becoming the first England boss to oversee four straight defeats and further puncture the feel-good factor of a run to the World Cup semi-finals.
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