Cristiano Ronaldo's goal has given Real Madrid a 1-0 lead over Granda at the half-time interval.
The hosts have dominated possession in the first 45 minutes and could be further ahead had Jose Maria Callejon and Ksrim Benzema not squandered glorious early chances.
The breakthrough came in the 26th minute when Callejon released Ronaldo inside the area and the Portuguese forward struck at goal from a tight angle.
The ball squeezed between Tono and the post to give Los Blancos the lead.
Granada found their footing as the half wore on and began to frustrate Madrid in the final third.
