The result is their heaviest ever defeat, the first time they have conceded six goals and the first game in which they have let in five since a 5-1 loss to England in 2009.
Vrsaljko provided Ivan Perisic with another chance during Croatia's early barrage but Spain's own right-back came to the rescue as Dani Carvajal tracked the Inter Milan winger to make a crucial intervention 10 yards from goal.
La Roja never looked back after Saul Niguez's headed opener.
Marco Asensio was their outstanding performer with one goal - Spain's second, driven in from 25 yards - and three assists.
In the World Cup final, Vicente del Bosque put out six Barcelona players (Puyol, Pique, Busquets, Xavi, Iniesta and Pedro) along with Villa who had just signed from Valencia.
Luis Enrique couldn't have asked for a much better start as coach of Spain's national team.
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.
Croatia will hope to get their first Nations League points when they host England next month. The Manchester United striker then added a third with a deft flick nine minutes from fulltime. During the Russia World Cup, they were the most represented club with six players.
In other Uefa Nations League games, England edged Switzerland 1-0, Belgium beat Iceland 3-0, and Poland and Ireland played out a 1-1 draw.
The hosts took their foot off the gas for the final quarter of an hour although Rodrigo and Isco still had chances to pile more humilation on Zlatko Dalic's side, who were handed a stark reality check on the back of their run in Russian Federation.