Diego Simeone's side appeared set for a frustrating evening after struggling to create clear chances for much of the match, but Alejandro Grimaldo, Jonathan David and Giuliano Simeone struck late to secure a valuable away victory.
• Real Sociedad: No goals
• Atlético Madrid: Alejandro Grimaldo 82' (pen), Jonathan David 90', Giuliano Simeone 90+4'
The match remained goalless for more than 80 minutes, with Real Sociedad enjoying periods of possession but failing to seriously test Jan Oblak in the Atlético goal.
The visitors also struggled to find their rhythm in attack during the opening hour. Simeone's changes, however, eventually transformed the contest, with Jonathan David and Koke among those introduced as Atlético looked for a breakthrough.
The decisive moment arrived in the 82nd minute when Real Sociedad midfielder Job Ochieng was penalised for handball inside the area. After the incident was reviewed, Atlético were awarded a penalty and Grimaldo stepped up to send Álex Remiro the wrong way and give the visitors the lead.
The goal opened the game up. Real Sociedad were forced to push forward in search of an equaliser, leaving spaces for Atlético to exploit on the counter.
Jonathan David made the most of one such opportunity in the 90th minute. The Canada international received the ball inside the area, cut inside his marker and calmly finished with his left foot to score his first goal for Atlético Madrid.
There was still time for Atlético to add a third. In the final moments, Giuliano Simeone embarked on a powerful run towards goal before finishing to complete a 3-0 victory and cap a remarkable late collapse for the home side.
The scoreline was harsh on Real Sociedad, who had competed well for much of the contest but were undone once Atlético finally found the breakthrough. The victory also gave Simeone's team a much-needed boost after a difficult start to the campaign.
For Atlético, the performances of Grimaldo and David were particularly encouraging, with both summer arrivals registering their first goals for the club. Giuliano's late strike provided the finishing touch as Simeone's team showed their ability to punish opponents once spaces appeared.
Real Sociedad, meanwhile, were left to reflect on a match that had been within their control for long periods before three late Atlético goals turned a competitive encounter into a heavy defeat.