After last week's defeat at home to Bayern Munich in the Champions League, where the Germans won 3-0, Barca lost points again in La Liga.
Granada's midfielder Domingos Duarte met the ball with his forehead, when the team lingered after a corner.
That goal was about to give Granada three points.
But Barcelona's onslaught would eventually pay off when Ronald Araujo equalized in the 90th minute and saved points.
Barcelona was on for more but never got really close. After four games played, the team is in seventh place, albeit with one game less played than five of the teams above and five points up to league-leading Real Madrid. Granada has scored three points after five games and is in 17th place.