Karim Benzema's first La Liga goal since March has given Real Madrid a 1-0 advantage over Cordoba from what was the two clubs' first 45 minutes of the new season.
With debutants James Rodriguez and Toni Kroos included in the starting lineup, hosting Madrid started brightly and they had a good chance to break the deadlock in the sixth minute, but Cristiano Ronaldo sent his headed effort wide of the target.
Then, just 60 seconds later, the away side created an opening, but with time and space inside the Madrid area, Mike Havenaar dragged his low shot wide of the left upright.
Kroos, Ronaldo and Sergio Ramos then all tried their luck as the home side started to dominate proceedings, but they were all denied by Juan Carlos in the Cordoba goal.
However, he was powerless to prevent Benzema from scoring the game's opening goal in the 30th minute as the Frenchman rose highest to convert Kroos's corner via the upright.
Despite more Madrid pressure in the minutes that followed, newly-promoted Cordoba, who are playing at the Bernabeu for the first time in 42 years, held out before the break.