Winger Griezmann produced a superb performance to guide Jagoba Arrasate's side to a comfortable victory that leaves them within six points of fourth-placed Athletic Bilbao, while Elche are just two points above the relegation zone.
The Frenchman opened the scoring after just three minutes with a lofted finish after he had latched on to an excellent ball from former Arsenal man Carlos Vela.
Sociedad's lead was doubled nine minutes later as the 22-year-old headed home a magnificent right-wing cross from Xabi Prieto.
And the game was put beyond all doubt five minutes into the second half as Mexican Vela found the back of the net with a curling effort from the edge of the area.
The Basque outfit refused to take their foot off the gas, though, Griezmann volleying home to complete his treble on 74 minutes after Tono had failed to collect Imanol Agirretxe's delivery.
