His second strike bounced off the post and the back of goalkeeper Lovre Kalinic, who was awarded an own goal.
The ex-Barcelona coach replaced Fernando Hierro, who oversaw Spain's World Cup bid after the Spanish FA sacked Julen Lopetegui a day before the finals in Russian Federation.
He promised evolution, not revolution, and while his team still dominated possession, they were faster, more direct and less predictable in the final third.
They'd have seen Spain edge out England 2-1, with a largely impressive opening display under new boss Luis Enrique - and will now be raring to take on the Spanish themselves at Estadio Manuel Martinez Valero in Elche.
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.
U.S. says ICC ‘dead’ as it moves to ‘protect’ Israel
He added that the PLO had also asked the ICC's prosecutor to speed up a preliminary probe into other alleged Israeli war crimes. The Palestinians accuse the administration of dismantling decades of USA engagement with them by blatantly siding with Israel.
La Roja now top Group four in League A with six points, followed by England and Croatia respectively.
Asensio found the back of the net twice in stunning fashion as Spain thrashed Croatia 6-0 (!) in the UEFA Nations League.
Spain manager Luis Enrique has rubbished suggestions that only one Barcelona player started in their UEFA Nations League match against Croatia exclusively because of hard feelings towards his former employers.
Lukaku made it 2-0 to Belgium minutes later, firing a close-range shot on the rebound that was judged to have crossed the line before Birkir Saevardsson managed to clear. Saul and Asensio cut through Croatia's medium block with two precise passes, which left Rodrigo Moreno in an easy 1v1 to make it 4-0. Croatia and England are both pointless after one game.
The Croats were making their Nations League debut after playing European champion Portugal to a 1-1 draw in a friendly last week.
Spain were barely recognisable from the team that failed to break down Russian Federation in the last 16 but it should also be said they put six past Argentina, under Julen Lopetegui, in March. Spain was eliminated during the round of 16 of the World Cup, losing to Russian Federation on penalties after a 1-1 draw.