Real coach Jose Mourinho had warned that an opponent would soon pay for his side's recent goal drought and Depor were the whipping boys on a rain-sodden night at the Bernabeu.
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Cristiano Ronaldo, Mesut Ozil, Angel Di Maria and Gonzalo Higuain put Real 4-0 ahead by the 53rd minute before Depor defender Ze Castro stroked the ball into his own net.
Juan Rodriguez scored a consolation for the visitors and Ronaldo raced on to Xabi Alonso's pass to complete the rout as Real doubled their season's goal tally to 12 from six matches.
"We have to be happy with what was a very complete performance," Real midfielder Xabi Alonso said in a television interview.
"It was important to get the early goal and we're happy for the forwards above all."
Barca had earlier failed to capitalise on a clinical Lionel Messi strike at home to Real Mallorca and the champions conceded a soft goal just before half-time to draw 1-1 at the Nou Camp.
Real have 14 points, two behind leaders Valencia, who secured their place at the top for another week when Aritz Aduriz and Vicente netted in a 2-1 home win over Athletic Bilbao on Saturday.
Villarreal are second on 15 after they recorded a fifth successive victory by beating Racing Santander 2-0 thanks to goals from Nilmar and Giuseppe Rossi.
Barca have 13 in fourth, one ahead of Sevilla. Alvaro Negredo scored one and created another to inspire the Andalusians to a 3-1 home win over Atletico Madrid on new coach Gregorio Manzano's home debut.
TRANSPARENT RAINCOATS
With the Real faithful sporting transparent plastic raincoats, Mourinho's Portuguese compatriot Ronaldo set Real on their way against Depor in the fourth minute.
The former World Player of the Year, who has had a difficult start to the season, headed powerfully past goalkeeper Manu from a corner.
New fan favourite Ozil weaved into a scoring position and drilled home in the 24th and Di Maria finished off a swift break with a spectacular header 10 minutes later.
He turned provider for Higuain eight minutes into the second period, lifting a cross over Manu for his Argentina team mate to volley into the empty net.
Barca were stunned 2-0 at home by promoted Hercules last month and Mallorca, coached by former Barca player Michael Laudrup, checked the Catalans' title defence again.
Messi celebrated picking up his European Golden Shoe trophy by scoring the opening goal, curling a shot into the corner of the net from just outside the penalty area.
After Messi went close to doubling Barca's lead, Mallorca midfielder Gonzalo Castro forced a fine save from Victor Valdes on a rare foray by the visitors and they were level from the resulting corner.
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