Goals from Marco Asensio and Nacho gave Carlo Ancelotti’s side an early lead, but Granada’s Luis Suarez pulled a goal back just before half-time.
Winger Vinicius Junior restored Los Blancos’ two-goal advantage shortly after the restart with Monchu then sent off for the hosts in the 67th minute.
Ferland Mendy wrapped up the win for the visitors, adding a fourth after 76 minutes.
The win meant Real Madrid climbed above Sevilla and Real Sociedad to the summit of La Liga.
Meanwhile, strugglers Granada dropped into the bottom three on goal difference.