Los Che were left ruing a number of chances in the first half as they succumbed to their second home defeat while the resolute Basque side move further clear of the drop zone
In an otherwise lackluster match, the Frenchman put Sociedad ahead when he reacted brilliantly to his own rebound lifting the ball over a stranded Diego Alves.
Los Che, determined to find an equalizer, attempted to break through a resolute Sociedad defense but Claudio Bravo's goal remained impenetrable as the league strugglers hung on to a surprise victory.
In a frantic start to the match Valencia wasted numerous opportunities to take the lead, with Roberto Soldado's replacement Aritz Aduriz unable to convert his chances.
Valencia's top scorer was suspended for Sociedad's visit, and Los Che missed his impressive strike rate as his deputy was denied twice by Bravo in the opening moments.
Aduriz did manage to beat the goalkeeper when he directed Dani Parejo's corner toward goal but it clipped the top of the crossbar on its way behind.
The Basque side succeeded in escaping the first half hour unscathed and grew in confidence as the half progressed. However, Philippe Montanier's side was unable to create much in the way of chances despite pressurising Valencia's goal.
Unai Emery's side returned from the break with a fresh impetus was both Pablo Hernandez and Sofiane Feghouli had early efforts on goal.
With neither side able to find the piece of creativity that it needed to force an opening, Real Sociedad launched an emphatic counter attack with Griezmann smartly lifting the ball over Alves into the back of the net.
Valencia attempted to find an immediate response but Sociedad was defending resolutely as it continued to threaten on the counter preventing an attacking onslaught from the home side.
Griezmann came close to doubling Real's advantage as he took aim from distance but his swirling effort, which had Diego Alves scrambling, went wide of the target.
Los Che strained to find a late equalizer but the home fans were left frustrated as a seemingly below par performance ended in defeat. Valencia faces city rival Levante next in its Copa del Rey quarterfinal tie and will be hoping to rediscover its scoring form, which had seen it net in all but two marches before tonight.
Montanier's side meanwhile hosts Atletico Madrid in a weeks time as they continue to look to escape the clutches of relegation.