Buoyed by winning their fifth FIFA Club World Cup by beating Al-Hilal in a thrilling final last week, Real started the game in blistering style. Elche failed to clear a Karim Benzema flick towards goal convincingly and Eder Militao was inches wide with a thunderous shot.
Moments later, Los Blancos took the lead as Marco Asensio danced through the visiting defence to slot past Elche goalkeeper Edgar Badia.
Despite winning their first league game of the season against Villarreal last time out, Los Franjiverdes were on the backfoot immediately as they searched for a route back into this game.
With the chances coming thick and fast for the hosts; Benzema should have done better placing a header wide inside the six yard box, while Federico Valverde’s side-footed effort was tipped wide by Badia.
Just after the half-hour mark Elche defender Enzo Roco handled in the area and conceded a penalty, which Benzema duly converted. The Frenchman would have another chance to finish from 12 yards before the interval, after Rodrygo was tripped inside the area.
As ever, his strike was clinical to give the defending champions an unassailable lead with his 11th league goal of the campaign.
The second half maintained a familiar pattern from the first, with Badia saving efforts from Rodrygo, Benzama and Asensio as Los Blancos sensed a big winning scoreline.
Elche brought on striker Lucas Boye, but it was more of a token gesture than to get back into the game and had little effect on their output.
After Benzema was replaced, another legendary figure stepped up to wrap up the contest as Luka Modric fired an unstoppable effort past a helpless Badia.