Barcelona scored two late goals to keep their 100 percent record intact as Real fell eleven points behind their bitter rivals after their game with Rayo Vallecano was postponed.
Xavi thumped a strike into the top of the net with just three minutes remaining, before a Lionel Messi cross was turned into his own goal by Borja Gomez, allowing the Catalans to grab all three points against an impressive Granada side.
That win left Barcelona with 15 points from five games, eleven points ahead of Real, who have played a match less.
"Every victory is important," Dani Alves told Spanish television. "Maybe we struggled more than on other days but we have to know how to get through these games.
"It wasn't that we didn't play well, a lot of credit must go to our rivals. Their keeper has been superb and I have to congratulate him."
Real will have to wait to try and reduce the gap to eight points after their match at Rayo Vallecano as postponed due to floodlight failure. Rayo claimed the lighting had been sabotaged by miscreants, and despite their best efforts it could not be repaired in time for Sunday's game.
Real and Rayo, however, disagreed on when the game would be played, with the home side wanting the match to go on Monday at 8.00 p.m. local time, but Real, citing their heavy workload and the uncertainly of the lights, wants the match to be played in the evening.
"There were a huge number of fans waiting and we ask their forgiveness but we hope they understand that these are circumstances beyond the club's control," Vallecano president Raul Martin Presa told reporters.
"They came here with all the excitement in the world hoping to see their team play one of the best sides in the world.
"Unfortunately due to an act of vandalism we are not going to be able to enjoy this match tonight."
"We have a very packed calendar and Rayo obviously does not," Real director of football Miguel Pardeza added.
"We have absolutely no responsibility for what has happened here and we have to defend our rights.
"As we have no guarantee that we can play tomorrow at 8 p.m., 5 p.m. tomorrow is when we want to play."
In other games, Atletico Madrid continued their good form, edging out Real Valladolid, thanks to goals from Diego Godin and Radamel Falcao. The win took Atletico to 10 points from four matches.
Valencia suffered defeat at the hands of Mallorca, with Victor Casadesus and Javier Arizmendi scoring the goals in a 2-0 victory, while Obafemi Martins marked his debut for Levante with the winner against Real Sociedad.