Real looked in for a testing evening when Mikel Rico (22) cancelled out Karim Benzema's 19th-minute opener to reward the visitors for an encouraging performance.
But Sergio Ramos headed Jose Mourinho's side back in front on 34 minutes and the game was over as a contest when Gonzalo Higuain and Benzema scored within five minutes of the start of the second period.
Cristiano Ronaldo then added further gloss to the scoreline with the fifth goal two minutes from time.
The home side had already threatened through headers from Ronaldo and Ramos before Benzema opened the scoring at the end of a sublime move.
Ronaldo cheekily lifted the ball into Mesut Ozil, who flicked it behind him for Benzema to sweep the ball home from six yards.
However, Granada were far from overawed and equalised just three minutes later when Ikechukwu Uche's cross from the right was headed home from eight yards by Rico.
Rico then had a shot saved by Iker Casillas before Real edged back in front, with Ramos directing an excellent header into the bottom corner from Ozil's corner.
Uche flashed a left-foot shot just wide two minutes later as Granada went into half-time still with the chance of pulling off a shock result.
But they were caught napping at the start of the second half as Higuain made it 3-1 after just 71 seconds.
Marcelo looked to have lost the ball in the area but stretched to divert it to Higuain to fire back across goalkeeper Roberto into the bottom corner.
If that was not bad enough, Benzema then grabbed his second of the night a few minutes later, superbly controlling Ozil's long pass with his first touch before easily beating Roberto.
Granada never threatened to get back into the match and Ronaldo rifled in a fifth from the edge of the area in the closing minutes to complete the rout.