Xabi Prieto scored the only goal of the game on 53 minutes but was fortunate his effort was not disallowed for offside.
The victory took Phillippe Montanier's side up to fifth in La Liga table while Atleti surrendered second place to Real Madrid.
Atletico were marginally the better side in the first half but created few clear chances.
The best opportunity came after 12 minutes, when Diego Godin flicked a corner on to the far post which was met by Falcao but deflected out of play by Markel Bergarra, although the referee awarded a goal kick.
The only other opportunities were efforts from Cebolla Rodriguez, Arda Turan and Koke, none of which troubled Claudio Bravo in the Real Sociedad goal.
The visitors, meanwhile, created even fewer chances in a half in which both teams played with a lot of caution.
Diego Costa came close to giving Atletico the lead not long after the re-start, running into the area on the left hand side and shooting just before reaching the byline, but the angle proved too tight for him and his chipped effort went just beyond the far post.
The ball did not go out and Real Sociedad launched a quick counter attack.
Antoine Griezmann pumped the ball up the pitch for Prieto to run on to. The forward was in an offside position but played to the whistle, ran into the box unchallenged and shot through the legs of Thibaut Courtois to give the Basques the lead.
It was the first time Atletico had conceded a goal in the league at the Calderon since October 28.
Diego Simeone's side put all their efforts into searching for an equaliser but were still unable to break down the organised Basques.
Falcao almost scored a goal with his hand after a free-kick by Koke but his effort was stopped on the line by Asier Illarramendi, and Miranda failed to convert the rebound.
Diego Cebolla and Koke then both pulled long distance efforts wide and Falcao chipped an effort just over the bar.
The visitors could then have doubled their lead when Atletico substitute Adrian Lopez headed a free-kick just wide of his own goal.
Atletico's final chance was created by Arda. The Turkey international cut inside from the left wing across the box but fired his shot just wide of the far post.
Even the presence of Courtois in the box for an injury-time corner could make no difference as the visitors stood firm to record a victory that takes them closer to Champions League football.
Real Sociedad are level on points with Malaga, who are the subject of a UEFA imposed ban from European football which, if upheld, would see Montanier's side qualify for Europe's elite competition if they can retain fifth spot.