Cristiano Ronaldo struck his 14th league goal in his last 10 appearances just before the hour and Karim Benzema made sure with 15 minutes remaining.
The victory opens up a two point-gap over rivals Barcelona and Atletico Madrid, who have a game in hand, at the top of La Liga.
The home side struggled to find a way past Ricardo in the Granada goal in the first half with Ronaldo, Sergio Ramos and Benzema all wasting good openings.
Ronaldo's 22nd league goal of the season broke the deadlock after the break, much to the relief of the crowd, with Benzema converting from a Marcelo pass to seal the points, although the victory was overshadowed by an injury to Gareth Bale that saw him substituted at halftime.
Granada failed to force a save out of Diego Lopez and the club's two-game unbeaten run comes to an end, with Lucas Alcaraz's side remaining in 10th place.
Carlo Ancelotti named the same side for a third consecutive league fixture, with Angel Di Maria starting ahead of Isco, while the visiting team made a single change as Mohammed Fatau replaced Fran Rico in midfield.
Ronaldo had the first opportunity for Madrid in the sixth minute, the Portugal international making something out of nothing as he cut in from the left but skewed his shot wide after beating two defenders.
Ramos went even closer five minutes later as the defender rose to meet a Bale delivery, but the center back headed over from close range.
Granada was doing a good job of restricting its opponents and Madrid had to rely on set pieces to threaten.
The home side had the ball in the back of the next just before the half-hour mark as Benzema turned in a knock down from Ramos, but the French striker was flagged offside and the goal was ruled out.
Ronaldo was denied on the stroke of halftime as his overhead kick from seven yards was brilliantly kept out by Ricardo.
Luka Modric and Benzema both wasted chances early in the second half, but in the 56th minute Ronaldo finally broke the deadlock.
The forward receiving a pass from Modric inside the penalty area, he was allowed to turn and fired low beyond Ricardo to relieve the pressure inside the Santiago Bernabeu.
After Ronaldo had seen a free kick hit the crossbar, Madrid doubled the lead in the 75th minute, Marcelo squaring a pass to Benzema to turn home from close range.
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