Zinedine Zidane’s side were 4-0 up after 32 minutes, with Isco slotting in their first from Karim Benzema’s pass.
Benzema converted after Guillermo Ochoa spilled a Luka Modric shot, before Cristiano Ronaldo headed a third.
Isco tapped in a Modric cross, and midfielder Casemiro touched home a fifth from James Rodriguez’s free-kick.
Who will stop Real Madrid this season? Zidane’s side have not lost a competitive fixture since Wolfsburg defeated them in the first leg of their Champions League semi-final last April.
Victory here was never in doubt, as a rapid start against relegation-threatened opponents took them six points clear at the top of La Liga.
They had a little bit of luck along the way. Benzema’s goal, Real’s second, should have been ruled out, as the France forward was clearly offside as he converted a loose ball pushed into his path.
But had it not been for Granada’s Mexico international keeper Ochoa, who made fine second-half saves from Dani Carvajal and Marcelo, the margin of victory would have been even bigger.