Asensio, who was not among the starters against England, also set up Rodrigo's goal early in the second half with a ideal through ball behind the defence.
"We played a spectacular game and rounded off a brilliant week".
"The truth is we had a great game". 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.
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Spain boss Luis Enrique is set to give Iago Aspas another place in the starting XI following his impressive display against the Three Lions at Wembley.
The two nations are facing each other for the seventh time, with Croatia taking the last meeting - a 2-1 win at Euro 2016.
Croatia could do little to stop the Spanish onslaught as the World Cup finalists suffered their worst ever defeat in team history.
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.
Saul Niguez, who is becoming an undisputable starter in Enrique's team, headed in a cross by Dani Carvajal in the 24th minute, then Marco Asensio hit two remarkable long-range shots in the 33rd and 35th to give La Roja a comfortable lead before halftime. Asensio scored two awesome goals.
More importantly, they are off to a winning start under Luis Enrique, with their performances in Elche and against England at Wembley a stark reminder of the quality they possess, which seemed to go missing in their tempestuous World Cup campaign.