Carlos Vela and Willian Jose each converted from the spot to give the home side the three points, while Real Madrid and Barcelona could pull ahead of the visitors in the table.
Atletico Madrid’s LaLiga title challenge suffered a major setback after they were beaten 2-0 by Real Sociedad at Anoeta courtesy of second-half penalties from Carlos Vela and Willian Jose.
Former Arsenal forward Vela coolly converted his fourth goal in 11 league outings after Gabi had clumsily fouled Yuri before Brazilian Willian Jose added a second with 15 minutes remaining as Atletico suffered their second defeat of the season.
Saturday’s setback means Atletico will be six points behind city rivals Real Madrid if Zinedine Zidane’s men see off Leganes as expected on Sunday.
The visitors were looking at Antoine Griezmann to make the difference against his former team, with the Frenchman scoring three goals in four LaLiga games against Real since his move to the Vicente Calderon in 2014.
The 25-year-old had netted six goals in nine league appearances heading into the encounter and was high on confidence following his double in the 2-1 Champions League win over Rostov on Tuesday.
But he did not make much of an impact, failing to test home goalkeeper Geronimo Rulli throughout.
There were chances for Kevin Gameiro and Yannick Ferreira Carrasco, but neither found the net as Eusebio Sacristan’s men secured a win which maintained their encouraging start to the season.
Real made a promising start and could have grabbed an early lead through David Zurutuza, the midfielder aiming just over the crossbar from the edge of the box after some good work from Vela down the right.
Atletico slowly grew into the game and could have opened the scoring in the 26th minute following some unconvincing goalkeeping from Rulli. The Real stopper failed to adequately deal with Griezmann’s cross from the left to allow Saul Niguez to try his luck, only for Rulli to make amends with a fine save.
Gameiro did manage to beat Rulli just minutes later after Asier Illarramendi lost possession inside his own half, but the Frenchman was unfortunate to see his delicate chip hit the upright, before it was cleared to safety by the Real defence.
Vela then called Atletico goalkeeper Jan Oblak into action with a superb long-range strike that seemed destined to find the top corner, the Slovenian doing well to tip the ball over for a corner kick.
Atletico went in search of the opener early in the second half and got a chance to break the deadlock in the 52nd minute when Carrasco beat the offside trap after a clever throughball from Griezmann, but the Belgium international could only blast a powerful shot into the sidenetting from a difficult angle.
The hosts went a goal up three minutes later when Vela slotted home from 12 yards. Referee Alfonso Alvarez Izquierdo had no choice but to point to the spot after Gabi felled Yuri and the Mexico international gave Oblak no chance with a low shot into the right corner.
Things went from bad to worse for Atletico in the 75th minute when the official awarded Real another penalty after substitute Angel Correa fouled Vela. Willian Jose stepped up this time and made no mistake to seal the win for the home side.