Rumours of Gareth Bale's impending arrival in Madrid had somewhat overshadowed the build-up to the game, but the visitors didn't appear distracted as Karim Benzema opened the scoring after just 10 minutes.
Mesut Ozil then had a goal ruled out and Isco struck the post after the break as Madrid continued to have the lion's share of the chances.
However, Granada were denied a great chance to snatch a point five minutes from time when referee Javier Estrada Fernandez failed to spot a trip on Diego Buonanotte by Casemiro inside the area.
Real boss Carlo Ancelotti's decision to keep faith with Diego Lopez in goal ahead of Spanish captain Iker Casillas was the big news before kick-off, but the Italian picked a very attack-minded line-up with Angel Di Maria coming in for the injured Sami Khedira and the former Milan boss was rewarded with a very bright start by his side.
Benzema should have put Real in front after just five minutes when he skewed wide after a lovely reverse ball from Di Maria had played him in.
The Frenchman made amends five minutes later though as Di Maria's cross from the right was inadvertently knocked into Benzema's path by Cristiano Ronaldo and he swept home from close range for his second goal of the season.
Ozil then had what would have been a lovely second goal ruled out as Fernandez adjudged the ball was still moving when Di Maria sent a quickly taken free-kick over the top for the German international to lob over Roberto.
However, Madrid's natural attacking instinct was also leaving them susceptible to the counter-attack and Youssef El-Arabi had a great chance to equalise on 19 minutes, but Alvaro Arbeloa just got the slightest touch to take the sting out of the Moroccan's effort and Lopez made a comfortable save.
Granada boss Luis Alcaraz replaced El-Arabi with summer signing Riki at the break and his presence gave the hosts more to aim at in the second-half.
Piti should have hit the target with a hooked effort from inside the area after Lopez had flapped at a high ball under pressure from Pape Diakhate.
However, Madrid still posed a threat themselves as Isco came within inches of a magical second as he cut inside and fired a shot off the outside of the post.
Ronaldo also had a decent opening 13 minutes from time but could only fire straight at Roberto as his search for his first goal of the season continued.
And the home fans and players were left furious in the closing stages as Buonanotte weaved his way along the by-line and seemed to be clipped from behind by misjudged challenge by Casemiro.
However, Fernandez was unmoved and Madrid held on to join Barcelona, Atletico Madrid, Athletic Bilbao and Villarreal at the top of the table with full points from two games.