"Croatia are the World Cup runners-up and all teams will be motivated against us - and we have to be aware of that".
Croatia, for whom Ivan Rakitic was making his 100th appearance, rarely got to grips with their opponents and conceded three times more in the second half through Rodrigo Moreno, Sergio Ramos and Isco.
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. Luis Enrique later added the player to the group after Diego Costa requested permission to leave the team to be present at his daughter's birth.
That counted as one of four assists for Asensio on the night, with a more conventional one coming four minutes after the restart when he released Rodrigo who nutmegged Kalinic for his fourth goal in six starts for his country.
Aspas, who has scored six goals in 14 appearances for La Roja, has been a big hit in Spain since returning to La Liga following his spell at Liverpool.
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What does it mean? He's a key part of Luis Enrique's Spain team and has returned the confidence shown in him by his coach. It made it two wins out of two for Luis Enrique's side in their Nations League campaign. 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.
His first goal was emphatic and he deserved his second effort to go straight in, rather than deflect off the back of the keeper.
The centre-back was consistently excellent in Russian Federation but was given a torrid time here.
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.
Spain's next match takes place in exactly a month, when they visit Cardiff for a friendly match four days before hosting England in the Nations League.