Dorlan Pabon grabbed a consolation goal for Valencia in injury-time as they lost for the first time since their shock 3-0 defeat by Swansea in the Europa League.
That loss had heaped the pressure on manager Miroslav Dukic, but he had ably turned fortunes around in a run of four wins from five games before Sociedad's visit.
The San Sebastian club therefore made the long journey south as underdogs and had to ride their luck in the first half before taking the lead.
Valencia striker Helder Postiga fired over from six yards with 12 minutes on the clock before Pabon forced Sociedad goalkeeper Claudio Bravo to save his 25-yard attempt.
Pabon then shot over from range and Bravo was at full strength when he denied Ever Banega's stinging drive.
After soaking up the pressure Sociedad struck the sucker punch four minutes before half-time.
David Zurutuza headed the ball into the centre of the area for Griezmann to drill a left-footed shot high into the net.
After taking an unlikely lead into the break Sociedad then doubled their advantage after 58 minutes.
Carlos Vela was the provider on this occasion as he worked the ball from the left flank for Pardo, who rifled home a powerful 25-yard strike.
Valencia tried to get back into the game but Federico Cartabia shot over and Pabon headed wide before getting a goal back, albeit with too little time remaining to mount a comeback.
The Colombia international picked his spot into the bottom-left corner from 12 yards after Dani Parejo's assist.