The hosts looked the stronger side from the start, with Daniel Hernandez in the Valladolid goal being forced into several saves inside the opening half hour.
Sociedad doubled their advantage six minutes later, as Imanol Agirretxe got the better of Hernandez with a strike from the centre of the penalty area.
A third for the hosts and a second for Griezmann ensured that they took a comfortable lead at half time.
Alvaro Rubio and Manucho both had chances to reduce the deficit for the visitors, but it was not until the 87th minute that Valladolid found a consolation goal, Javi Guerra tapping home an Oscar cross.
The win moves Real Sociedad into the top four, while Valladolid drop to 12th.