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.
Spain made three changes to the team that won at Wembley, bringing in Valencia defender Jose Gaya and Real Madrid pair Dani Ceballos and Asensio.
Their inclusion made Luis Enrique the first Spain coach in 16 years to name six Real Madrid players in a starting lineup, making a mockery of fears in the Spanish media when he was appointed that he would discriminate against Real players over loyalty to his former club Barcelona.
Real defender Dani Carvajal made a decisive block early on to thwart Croatia forward Ivan Santini as Zlatko Dalic’s side made a bright start and caused plenty of unease for Spain, who lost 2-1 when the teams last met at Euro 2016 in a group game.
Carvajal also provided the cross from which Saul headed the opener, giving Spain a huge injection of belief and rattling the visitors, who moments later conceded possession in midfield before Asensio smashed the loose ball home from long range.
Croatia, so impressive in keeping the ball at the World Cup, lost confidence as Spain dominated possession and picked their opponents off with ease, inflicting biggest defeat on the Croats after a 5-1 loss to England in a World Cup qualifier in 2009.