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.
Mario Mandzukic missed two clear chances in the first half for Atletico, whose Spanish Super Cup victory last Friday over Real appeared to take its toll as the players looked fatigued in the second half.
Atletico’s Argentine coach Diego Simeone was absent from the touchline due to a ban from last season and he has been given a further eight-match sanction on Monday for his dismissal and angry reaction in the Super Cup.
Benzema struck on the half-hour for Real with a badly needed goal having only scored once in the previous 15 games.
Cordoba did unsettle the home side in the second half but Ronaldo hit a 25-yard drive into the corner to settle the game in the final minute.
A new look Barcelona with Luis Enrique taking charge following a season without a major trophy beat Elche 3-0 on Sunday.