Three first-half goals put Sociedad in the driving seat and despite a couple of consolation goals, they take three important points as their unbeaten run continues.
The home side started the game well, controlling possession and pressing high up the pitch without ever finding the right pass in the final third.
It didn't matter though, as a minute later they were ahead. Malaga failed to deal with a corner, allowing Carlos Vela to find space and tap the ball in from close range.
They doubled their lead three minutes later. Left-back Alberto de la Bella was allowed to run free in the visitors' half, picking up the ball and firing it into the bottom corner from outside the box.
Things got even worse for Malaga five minutes after that. Griezmann was again played in behind the defence, and this time tucked the ball away to give Sociedad a 3-0 lead.
Malaga did manage to give themselves a lifeline, when Pedro Morales found space outside the box and found the back of the net with a powerful shot on the stroke of half time.
Five minutes into the second half the home side scored again when an in-swinging corner was met by Inigo Martinez, who headed past the goalkeeper.
The home side regained a measure of control after that, but 20 minutes from time, Malaga scored again when Roque Santa Cruz found space in the box.
It was to be no more than a consolation goal though, and the win sees Sociedad move four points ahead in the race for fourth place.