Real failed to get moving for most of the first half, but took the lead on the half-time stroke as Eder Militao got into the box to go home at the end of a hazardous Marcelo delivery.
With Andriy Lunin and Victor Chust both delivering first-team debuts, Zinedine Zidane made wholesale improvements to his side, after the Spanish Supercopa semi-final loss to Athletic Club last week.
As the Spanish champions plunged to a 2-1 loss at the hands of third-tier CD Alcoyano, who ended the match with 10 men, Real Madrid suffered a disappointing exit from the Copa del Rey.
Ramon Lopez’s dismissal in extra-time seems to have given Real Madrid the edge, but Alcoyano’s 10 men scored a winner when Juanan nipped in to convert an Ali Diakite cross at the near post.
Vinicius Junior had an outstanding opportunity to bring the game beyond doubt, but Jose Juan saved his breakaway shot before Jose Solbes equalized with nine minutes left, prodding home from a corner at the back post.
CD Alcoyano – Real Madrid 2-1
Goals: Militao (45), Solbes (80), Juanan (115)
Córdoba – Real Sociedad 0-2