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.
Deportivo were left to rue to big chances missed by Florin Andone in the first 10 minutes, whilst the Romanian international also saw a late penalty saved by Keylor Navas.
Real boss Zinedine Zidane made four changes from the side that completed a 5-1 aggregate hammering of Barcelona in the Spanish Super Cup on Wednesday.
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.
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.
Ramos was then lucky to avoid a straight red card when he slapped Fabian Schar.
Andone missed another chance for a consolation when his poorly hit spot-kick was easily turned behind by Navas two minutes from time.
However, Real were denied a trouble free night when Ramos was finally dismissed for a second yellow card in stoppage time.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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