Cristiano Ronaldo's 23rd-minute own goal was enough to give new coach Lucas Alcaraz a dream start to life with the Andalusians.
Less than a minute later they were ahead when Gabriel Torje's corner was turned into his own net by Ronaldo.
Los Blancos were the better team for much of the second half, but their dominance went unrewarded as they created very few clear-cut chances.
The away side's best chance fell to Karim Benzema with five minutes remaining, but the French international striker fired wide of the target with the goal at his mercy.
The victory was the first time Granada have beaten the nine-time European Cup winners in 40 years.