Carlos Vela opened the scoring nine minutes into the second-half before handing responsibilities from the spot to Willian Jose to seal Sociedad's third straight win 15 minutes from time.
A second league defeat in three games means Atletico remain three points behind league leaders Real Madrid, but their city rivals can extend that advantage to six when they host Leganes on Sunday.
Atletico host Real in a rematch of the Champions League final after the international break on November 19.
Diego Simeone's men had sealed their place in the last 16 of the Champions League on Tuesday with a stoppage time victory over FC Rostov, but suffered a European hangover in an insipid display lacking in energy and invention.
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Sociedad dominated possession in the opening 20 minutes, but it was Atletico who had the best chance before half-time when Kevin Gameiro was played in by Yannick Carrasco and was unfortunate to see his chip over Geronimo Rulli come back off the post.
A tight game swung decisively Sociedad's way when left-back Yuri burst into the box just after the break and was upended by Atletico captain Gabi.
Vela stepped up to coolly sent Jan Oblak the wrong way for his fourth goal of the season.
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The Mexican blasted a great chance to seal the win over as Sociedad threatened to pick Atletico off on the counter-attack.
However, Vela was key for the second goal as he led another break and was chopped down by Angel Correa.
Jose also sent the helpless Oblak the wrong way from the spot to move Sociedad to within two points of Atletico in sixth.
At the other end of the table, Granada remain rooted to the bottom and without a win this season after a 1-1 draw at home to Deportivo la Coruna.
Florin Andone handed the visitors the lead, but an own goal from Deportivo 'keeper Przemyslaw Tyton salvaged a point for Granada nine minutes from time.
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