Real Madrid's slim hopes of regaining the Spanish La Liga title were all but extinguished by a defeat at Champions League hopefu
After a tight first half, Real Madrid fell behind when Eder Militao sold Thibaut Courtois short with a backpass and Takefusa Kubo slid into an empty net.
Madrid's frustrations spilled over as right-back Dani Carvajal was sent off for two bookings in quick succession.
The home side, made to tick by veteran midfielder David Silva, sealed a deserved win when substitute Ander Barrenetxea fired in a late second.
The loss leaves Carlo Ancelotti's side 14 points behind rivals Barcelona with just five games left to play.
Earlier on Tuesday, Barca overcame 10-man Osasuna's stubborn resistance to earn a 1-0 win through Jordi Alba's late strike.
In a match where they needed to win to keep pressure on Barca, Madrid were without a host of key players - striker Karim Benzema, winger Vinicius Junior, midfielder Luka Modric and centre-back David Alaba - against fourth-placed Real Sociedad in San Sebastian.
With the title looking out of reach, Madrid realise their best chances of silverware this season come elsewhere and already seemed to have an eye on Saturday's Copa del Rey final against Osasuna.
Three days after that, they host Manchester City in the first leg of their Champions League semi-final.
Despite the changes, Ancelotti's team started confidently against Real Sociedad and home keeper Alex Remiro produced a stunning save from Militao to stop Los Blancos taking the lead.
But Real Sociedad, who played with aggression and energy, started to take control and created good opportunities themselves before the break.
Home defender Martin Zubimendi stretched to poke against the crossbar instead of the gaping goal, but Real Sociedad continued to press and earned a deserved victory in the second half.
The three points consolidates fourth place for the Basque club, who are eight points clear of fifth-placed Villarreal as they close in on Champions League qualification.
Meanwhile, Elche's relegation from the Spanish top flight was confirmed with a 2-1 defeat at Almeria.
Goals from Leo Baptistao and Adri Embarba, either side of half-time, put the hosts in control before Ezequiel Ponce pulled one back in the closing stages for the bottom team.