Algerian Yacine Brahimi scored the only goal yesterday after 16 minutes as FC Barcelona failed to find a way past the inspired Orestis Karnezis in the Granada goal.
Defeat rounds off an awful week for FC Barcelona as they were also dumped out of the Champions League by Atletico Madrid on Wednesday.
The Catalans are now third in La Liga, a point behind both Real Madrid and Atletico after Real cruised to a 4-0 win over Almeria at the Santiago Bernabeu thanks to goals from Angel di Maria, Gareth Bale, Isco and Alvaro Morata.
Atletico, who now just need to win five of their remaining six games to claim a first La Liga title in 18 years, can open up a gap at the top when they face Getafe on Sunday.
"It is a step backwards. It was just one move, for their goal, which we were punished for despite all the effort we put in," FC Barcelona midfielder Andres Iniesta told Canal Plus.
"At times it is difficult to explain when you lose. We lacked goals, but the rest we had under control.
"They only had the one chance with their goal. Teams like this, that are playing for their lives, live off just getting one chance. It is undeserved, we ought to have won but we haven't done so.
"We did everything to score. All we lacked was the finish, which is the most difficult part and makes the difference."
FC Barcelona boss Gerardo Martino shared Iniesta's analysis of the game and said he couldn't fault his players' performance as they racked up 29 efforts on goal and enjoyed over 80 percent of the possession.
- 'Matters no longer in own hands' -
"We no longer have matters in our own hands, but I couldn't ask for anything more from the players," he said.
"They tried in every way possible. They created plenty of chances, but today it wasn't to be. I can't criticise them for anything apart from obviously not finishing off the chances we had."