Champions Atletico Madrid made a sluggish start to the defence of their La Liga title with a 0-0 draw against Rayo Vallecano while a header from Karim Benzema and a late Cristiano Ronaldo strike helped Real Madrid beat promoted Cordoba 2-0.
Real started well and began to raise the tempo with Ronaldo and Toni Kroos having shots from the edge of the area which Cordoba keeper Juan Carlos Martin dealt with comfortably and the pressure told with Karim Benzema's goal after 30 mintues - his second goal in 15 games.
The visitors made it difficult for Real after the restart and Xisco thought he had equalised midway through the second half but was called offside.
Ronaldo showed his quality by taking full advantage of the opening he had with a 25-yard drive into the corner to settle the game in the final minute.
For Atletico, Mario Mandzukic missed two clear chances in the first as the Spanish Super Cup victory last Friday over Real appeared to take its toll and the players looked fatigued in the second half.
"The team played very well, they could have scored in the first half and later what happened is normal. We played Tuesday and Friday last week and put in all that effort," Atletico coach Diego Simeone told a news conference.
"We were better in the first half and had three clear chances and Rayo improved in the second half and caused us problems."