It appeared European champions Real Madrid would emphatically put worries over a poor start to the season behind them when they flew out of the blocks, Gareth Bale's neat finish adding to Sergio Ramos' header to secure a 2-0 lead after 11 minutes.
But they missed a series of other chances during a dominant start and were made to pay the price as Inigo Martinez pulled a goal back.
Suddenly full of confidence, Sociedad took control thereafter, David Zurutuza's double added to by Carlos Vela to secure an incredible triumph.
It left Real Madrid on three points through two league games, while the win was Sociedad's first of the campaign.
A goal-fest was played out at Estadio Riazor, where Deportivo La Coruna and the visiting Rayo Vallecano drew 2-2 thanks to Isaac Cuenca's last-gasp penalty for the hosts.
