Nuno's side were chasing their fifth Liga win this season but were held to a draw by the Basque club, despite taking the lead through Carles Gil
However, this might be considered a point gained by Valencia, given the possession and opportunities created over the 90 minutes by their hosts.
Chasing a fifth successive La Liga win, following victories over Malaga, Espanyol, Getafe and Cordoba, Valencia were fortunate keeper Diego Alves was in such good form during the early encounters.
After just four minutes, the Brazilian was tested when Carlos Vela cut in from the right on to his favoured left foot, the Mexican seeing his shot parried by the Valencia shot stopper.
Alves then produced an excellent diving save, throwing himself to his left when Imanol Agirretxe let fly from distance.
However, against the run of play Valencia served notice of why they are flying so high in the league this term by taking the lead after quarter of an hour.
Antonio Barragan centred from the right, finding Paco Alcacer whose knockdown landed in the path of Carles Gil who struck a measured volley with the inside of the left foot past the previously untroubled Enaut Zubikarai.
Real Sociedad countered almost immediately, a telling Vela cross forcing a diving punch from Alves who again showed some of the form that earned him 16 clean sheets last term when he clawed out an Agirretxe snap shot from long range.
The scoreline belied the home side's territorial advantage during the first period and eventually their pressure and perseverance was rewarded with an equaliser after 37 minutes.
Firstly Sociedad defender Inigo Martinez saw his header cleared off the line by Jose Luis Gaya, but when the ball was knocked out to left field, Sergio Canales low centre was missed by the in-rushing Agirretxe and the Valencia defence, leaving a distracted Alves to watch as the ball crept in at his far post.
It was a deserved equaliser for the hosts given their first half effort.
Valencia coach Nuno Espirito Santo looked to change things at half-time, introducing Filipe Augusto and Sofiane Feghouli, but Real were still the more committed to attack.
Alves needed to keep his wits about him, acting as a sweeper to deny Carlos Vela, while Augusto’s first real contribution came after 67 minutes, a speculative shot from long range. Had Rodrigo’s centre not carried as much pace it may well have connected with Alcacer who for once had escaped his marker.
Sociedad coach Jagoba Arrasate decided to pitch in his big money summer purchase, former Heerenveen striker Alfred Finnbogason in an attempt to win the match.
In the final seconds both teams had chances, Valencia denied with a great close range stop by Zubikarai from Shkrodan Mustafi, who at the other end headed away a goalbound attempt from Canales.