The champions looked on course for a sixth straight win in all competitions when Mario Mandzukic fired them ahead early on.
However, Carlos Vela soon equalised and Guilherme Siqueira was sent off towards the start of the second half.
That gave Sociedad the inspiration to push on and end an eight-match winless run when Imanol Agirretxe headed home on 82 minutes.
With reserve coach Asier Santana in charge following the dismissal of Jagoba Arrasate, Sociedad secured just a second success of the season and moved out of the bottom three on goal difference.
Atletico are now fourth, while third-placed Valencia also failed to prevail when held to a goalless draw at home to Athletic Bilbao.
Valencia failed to maintain their 100 per cent record at Mestalla in La Liga this term as Ernesto Valverde's visitors showed good organisation and resilience at the back.
Those two results leave Real Madrid and Barcelona at the head of affairs following Saturday victories over Rayo Vallecano and Almeria respectively.
Sevilla also dropped points for the second straight week as they failed to hold onto the lead given them by Vitolo when drawing 1-1 at home to Levante, with Victor netting a 79th-minute equaliser for the visitors.
Espanyol and Villarreal shared the spoils 1-1 at Estadi Cornella-El Prat, with Diego Colotto levelling in stoppage time for the hosts after Mario Gaspar had earlier broken the deadlock.
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