Gonzalo Escalante nodded Eibar level from a corner in the 26th minute but the visitors were reduced to 10 men at the start of the second half when Florian Lejeune picked up a second booking.
Juanmi earned his second yellow card for a shirt tug just before the hour mark to restore numerical parity but Carlos Vela restored the hosts' lead in the 67th minute from the penalty spot after Inigo Martinez was felled by goalkeeper Yoel Rodriguez.
Eibar coach Jose Luis Mendilibar was sent from the dugout for protesting about the penalty decision but had something to celebrate at the end when Leon's low shot slipped under the grasp of Real Sociedad goalkeeper Geronimo Rulli.
Real Sociedad are fifth in the standings on 45 points, level with Atletico in fourth, with Diego Simeone's side visiting struggling Deportivo La Coruna on Thursday. Eibar are provisionally seventh on 39 points.
La Liga leaders Real Madrid host Las Palmas on Wednesday while champions Barcelona entertain relegation-threatened Sporting Gijon.
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