The home side looked set for all three points, but a late goal means they missed a golden opportunity to make headway in the race for fourth spot
Philippe Montanier’s men had the opportunity to pull back ahead of Valencia into fourth place, but the draw sees the two teams tied on 59 points with three games remaining.
Imanol Agirretxe gave Sociedad an early lead, heading the ball home from a free kick from a seemingly offside position, only for Youssef El-Arabi to level for the visitors just minutes later.
Agirretxe made it 2-1 to Sociedad and looked to have ensured his side secured all three points, but deep into injury-time Jose Recio fired home after poor defending from the hosts to conclude a dramatic climax.
While the draw is a damaging one for la Real's European aspirations, a point moves Granada four points clear of the relegation zone.
Sociedad now have just one win in their last four games and travel to Sevilla at the weekend, before facing Real Madrid and Deportivo in their final two games of the camapaign.