Diego Simeone's charges, who boast one of the best defences in the Spanish top flight, were picked apart by the inspired Basques at the Anoeta Stadium.
An erroneous offside decision denied Atletico a clear goalscoring opportunity on 41 minutes, a long ball over the top destined for Kevin Gameiro being flagged, but the hosts were worthy of being ahead come the break.
Atletico, meanwhile, now sit just three points ahead of bitter rivals Real Madrid in second, and 12 points behind leaders Barcelona with just five games left to play.
REAL SOCIEDAD (4-3-3): Rulli; Elustondo, Navas, Moreno, de la Bella; Canales, Illarramendi, Pardo (Zurutuza 65'); Januzaj, Jose (Bautista), Oyarzabal (Juanmi 72')
ATLETICO MADRID (4-4-2): Oblak; Juanfran (Vitolo 54'), Savic, Godín, Vrsaljko; Correa (Torres 45'), Niguez, Thomas (Fernandez 75'), Koke; Griezmann, Gameiro