Despite the introduction of Lionel Messi and Ansu Fati at half-time, the champions woes were further compounded after Arturo Vidal handled in the box.
Alvaro Vadillo added the hosts’ second from the penalty spot.
The result leaves Barcelona three points behind Granada in seventh and they have now failed to score in six of their last seven La Liga away matches.
It was a match that Barcelona ought to win as they had 74 per cent possession.
But they only had one shot at the goal, compared to the four shots by their hosts.
Barcelona are 7th in the league with 7 points, while Granada have 10 points at the summit.