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."
Ronaldo banned for five matches for pushing referee
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.
Ronaldo not going anywhere, claims Zidane
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.
In the other encounter earlier, Barcelona got their league season off to a winning start, beating Real Betis 2-0 at a emotional Camp Nou following a pair of terrorist attacks in Catalonia.
Twin vehicle attacks on Thursday killed 14 people and wounded around 120 in Barcelona's bustling Las Ramblas boulevard and the nearby seaside resort of Cambrils.
A minute's silence was held before kick-off, whilst Barcelona players wore black armbands and shirts with 'Barcelona' replacing individual names on the back.
"What happened was terrible, we hope this stops now because we are not afraid," Barca winger Gerard Deulofeu, who set up both goals, told BeIN Sports Spain. "This victory is for those affected."
The decision for the match to go ahead with increased security measures put in place was part of a desire to "recover normality" in the words of Catalonia's president Carles Puigdemont.
A defiant attitude was on show in the stands, although in common with many matches against weaker opposition, the 99,000 capacity Camp Nou was far from full.
After the attack some fans, especially tourists, returned their tickets, the club said without giving figures.
"Their money was refunded to everyone, the circumstances are special and understandable," said a club spokesman.
Prior to the attacks, Barca had endured a difficult start to the season on the field as shorn of Neymar following his world record €222 million move to Paris Saint-Germain (PSG), the Catalans were swept aside 5-1 on aggregate by Real Madrid in the Spanish Super Cup.
Coach Ernesto Valverde admitted on Saturday events in the past few days had put the club's problems into perspective.
However, despite also missing the injured Luis Suarez and Andres Iniesta, Barca rose to the challenge of raising the city's spirits with a dominant display.
"In the end you always have to move forward," said Valverde. "Our idea was to be able to dedicate this victory to those affected."
With the mayor of Cambrils Cami Mendoza and chiefs of Catalonia's regional police force among those watching on, captain Lionel Messi led by example with Deolofeu and Paco Alcacer struggling to fill Suarez and Neymar's shoes up front.
Messi smashed an early free-kick off the post and his presence was enough to pressure Alin Tosca to turn Deulofeu's low cross into his own net for the opener nine minutes before half-time.
Deulofeu was the provider once more when Barca doubled their advantage three minutes later as Sergi Roberto slotted home from close range.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ