The 6-0 scoreline was Croatia's biggest-ever defeat.
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.
Croatia, which lost the World Cup final to France, fell apart after defender Sime Vrsaljko had to be substituted due to an injury just minutes before Spain's first goal. "It was really good playing here", he said after the game. But Spain weren't finished, 8 minutes later, Serjio Ramos scored the 5th from a corner kick. He's a key part of Luis Enrique's Spain team and has returned the confidence shown in him by his coach.
Maybe rotations will allow him to squeeze them both into the same side but when the important games come around and there are no rotations, one of Isco or Asensio must sit on the bench, something which for them and supporters will be hard to understand.
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.
In the other League A match on Tuesday, Belgium won 3-0 at Iceland in its Nations League debut.
Spain have rattled in the goals against Croatia to take charge of their Nations League group.
Belgium began with nine of the players who started the World Cup third-place playoff win against England in Russian Federation, with the injured Kevin De Bruyne replaced by Dries Mertens.