The club from San Sebastian extended their unbeaten run to 10 games with a devastating display of attacking football that keeps them on course for a shot at European football next season.
Philippe Montanier's side moved to 47 points with 10 games left and into the last Champions League qualification berth, 10 points behind third-placed Atletico Madrid, who visit Osasuna on Sunday.
They pushed Champions League quarter-finalists Malaga, who host Espanyol on Sunday, down to fifth on 44 points.
Leaders Barcelona, with 71 points, host Rayo Vallecano on Sunday, while second-placed Real Madrid, with 58 points, are at home to Real Mallorca later on Saturday.
After a tight opening period, a Sociedad brimming with confidence scored three times in the last 16 minutes of the first half, the 21-year-old Griezmann tucking away the first from close range in the 34th.
Imanol Agirretxe curled a shot into the top corner soon after and Griezmann brought the house down with his strike just before the break.
He raced through the middle on to a long floated pass from David Zurutuza, controlled the ball with one touch, and before it hit the ground rifled a shot past Daniel Hernandez.
A scything move of one-touch passes started by Griezmann saw Xabi Prieto poke Sociedad's fourth straight after the re-start, and Ruben Pardo rattled the visitors' crossbar.
Valladolid snatched a well-worked goal through Javi Guerra at the end to stay 12th with 35 points.