Eibar opened scoring through friendly fire after Real Sociedad's Asier Illarramendi scored by mistake after 57 minutes,reports Efe.
Portuguese Tiago Manue Bebe scored the second goal nine minutes later to double the lead.
After Saturday's victory, Eibar provisionally holds fourth place with 10 points, while Real Sociedad is 10th with seven points.
Real Madrid leads La Liga with 13 points, just two points ahead of runner-up Sevilla and three points before third-place Barcelona.
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