David Moyes started the evening under pressure after leading his side to two draws and two defeats in their opening four league fixtures, but they made the perfect start by breaking the deadlock in the seventh minute.
A well-timed run from David Zurutuza allowed him to collect space on the wing, and his inviting cross was turned home by Agirretxe as Granada were punished for poor marking.
Sociedad grew in confidence after taking an early lead, before doubling their advantage when Doria's weak pass towards his own goal allowed Agirretxe to take the ball past Andres Fernandez and tap into an empty net.
However, Sociedad always appeared comfortable and they were dangerous on the break as Agirretxe fired just wide of the post after beating the offside trap.
There was still time for Agirretxe to complete his hat-trick 11 minutes from time as he collected a lobbed ball forward before evading a challenge in the box to slot home his third of the night as Sociedad climbed into the top half of the table.