Gareth Bale, Casemiro and Toni Kroos were on target for the visitors, but Madrid's night at La Riazor ended on a sour note.
Gareth Bale, Casemiro and Toni Kroos were on target for the visitors, but Madrid's night at La Riazor ended on a sour note when captain Sergio Ramos was shown the 23rd red card of his Real career.
"Clearly I am not happy with what happened with Sergio," said Madrid boss Zinedine Zidane.
"I don't like seeing my players get sent-off, but we can't change it now."
Ramos could have been dismissed earlier in the second-half when he only received a yellow card for a slap on Deportivo defender Fabian Schar.
However, he tied a record for 18 red cards in La Liga with a second booking for an elbow on Borja Valle in the dying embers of the match.
"In general we can be happy with our performance," added Zidane.
"It isn't an easy place to come and they had chances to score."
Deportivo were left to rue two big opportunities missed by Florin Andone in the first 10 minutes, whilst the Romanian international also saw a late penalty saved by Keylor Navas.
Zidane made four changes from the side that completed a 5-1 aggregate hammering of Barcelona in the Spanish Super Cup on Wednesday.
Victory in midweek sealed a fourth trophy for Zidane's men in as many months after lifting La Liga, the Champions League and UEFA Super Cup.
However, far from their invincible form of late, Real were lucky to escape unpunished from a slow start.
Navas flew to his left to turn Andone's first effort from a narrow angle to safety, but should have been beaten when the forward fired straight at the Costa Rican when clean through moments later.
There was no way back for Deportivo once Madrid took the lead on 20 minutes as Bale pounced on Karim Benzema's scuffed shot to fire into an unguarded net for his first goal of the season.
A wonderfully worked team goal followed six minutes later as Real moved the ball all over the pitch before Marcelo's low cross was turned home by Casemiro.
Bale turned provider for Real's third just after the hour mark as Kroos's deflected effort from the edge of the box found the top corner.
Andone missed another chance for a consolation when his poorly hit spot-kick was easily turned behind by Navas two minutes from time before Ramos saw red.
Madrid move to the top of the table thanks to their better goal difference ahead of Barcelona, who beat Real Betis 2-0 in emotional circumstances at the Camp Nou earlier on Sunday.
In Barca's first home match since a pair of terrorist attacks killed 14 people and wounded around 120 in Barcelona's bustling Las Ramblas boulevard and the nearby seaside resort of Cambrils, Barcelona players wore black armbands and shirts with 'Barcelona' replacing individual names on the back.
The hosts rose to the challenge of raising the city's spirits as an Alin Tosca own goal and Sergi Roberto's strike ensured a comfortable victory.