Jose Mourinho has already conceded defeat in the title race to Real's arch-rivals, and they now face a battle to overhaul cross-city foes Atletico in the battle for second place.
Cristiano Ronaldo was among the goals again on Saturday, but notched at the wrong end.
The Portuguese forward, so often the hero for Real, turned villain as he connected with a Gabriel Torje corner to put through his own net on 23 minutes.
Ronaldo has scored more goals this season than the entire Granada side combined, but he offered them an unexpected helping hand at Los Carmenes.
While reigning champions Real continue to struggle in the defence of their league crown, Granada have edged three points clear of the relegation zone.