The Los Blancos were without the rested Cristiano Ronaldo and the injured Gareth Bale but started blazing right from the kickoff, with Alvaro Morata scoring in the first minute and James Rodriguez made it 2-0 13 minutes later.
Florin Andone scored on the 35th minute to show some fight for the hosts but Lucas Vazquez gave the visitors a 3-1 advantage when he scored with a mite left in the opening half.
Zinedine Zidane’s side ramped the pressure up after the break, with Rodriguez completing his double in the 66th minute and Isco finding the net for Madrid 11 minutes later.
Joselu scored from an Andone assist on the 84th minute, but Casemiro made sure Madrid were the last on the scoresheet and scored three minutes from the closing whistles.
“I come away from here happy with the performance and everyone’s goals,” said Zidane. “The players that don’t get as many minutes are also focused and fitness-wise you couldn’t spot any difference, quite the opposite.”
Real are tied with Barcelona in the top of La Liga table but the Madrid side have a game in hand.
Madrid, who will win the title if they sweep their remaining games, have not won the league since 2012, while Barca lifted the league trophy in the last two seasons.
The capital side are also in the hunt to defend their Champions League title and will host cross-town rivals Atletico Madrid in the first leg of their semi-final clash.
Barcelona got kicked out of the European competition after getting shut out over two legs by Juventus, but can still nip Real to the tile and beat Deportivo Alaves in the Copa Del Rey final for their third straight domestic double.