In a match of precious few chances at the Estadio Nuevo Los Carmenas, the hosts bounced back from shipping four against Malaga last weekend and moved out of the relegation zone on goal difference after the stalemate.
But manager Juan Antonio Anquela will hardly be buoyed by his side's lack of goals although they had their chances tonight.
Anquela was under some pressure for a result this evening after his team were booed off the pitch in their last home match against Espanyol and the Malaga result will have heightened tensions further.
They had a brilliant chance to end their goal drought early on when on-loan forward Odion Ighalo fired over the bar from Dani Benitez's low cross.
Xabi Prieto had earlier shot tamely at Granada keeper Fernandez Roberto, while Diego Ifran fired wide of the target from just outside the area as Sociedad, unbeaten in six in all competitions before tonight, looked the more threatening.
It took a marvellous save from Roberto to keep the scores level after Diego Ifran had headed Carlos Vela's ball into the area goalwards.
Sociedad continued to be in the ascendancy after the interval and Fernandez fumbled a vicious 20-yard strike from David Zurutuza before his defenders came to the rescue and cleared the ball away.
Asier Illarramendi should have done better when he struck over from the edge of the box and his miss nearly came back to haunt him following a rare Granada attack.
Ighalo got goalside of his marker and latched on to Benitez's through ball but was unable to strike either side of on-coming Sociedad keeper Claudio Bravo.
It was by far the best opportunity of the match but the poor finish summed up the hosts' woes.