La Real remain unbeaten, Espanyol pull off a fine victory against Valencia and Villarreal show they are ready to compete in the top flight
Real Sociedad failed to cap off their impressive week as they drew 1-1 with Liga newcomers Elche.
Having beaten French giants Lyon 2-0 in the Champions League play-off on Tuesday, Real fell behind after two minutes as a corner snuck through goalkeeper Claudio Bravo at the near post and Coro was on hand to finish into the empty net.
Elche fought valiantly but former Arsenal attacker Carlos Vela grabbed the equaliser 15 minutes from time when his scuffed finish from Xabi Prieto's cross did enough to find the back of the net.
Meanwhile, Espanyol's solid start to La Liga has continued as they came from a goal down to beat Valencia 3-1 at the Estadi Cornella-El Prat.
After coming from two goals behind to draw with Celta Vigo on the opening weekend, Espanyol conceded first again after only 10 minutes when Valencia's Jonas held the ball up in the penalty area and laid it off to Helder Postiga, who clinically smashed his shot past goalkeeper Kiko Casilla.
Valencia held their lead until the 32nd minute when an Espanyol corner from Simao was headed home at the near post by David Lopez.
But los Che's frailties from set pieces were again exposed by Espanyol as Christian Stuani headed home Juan Fuentes' free-kick unopposed.
Despite conceding large amounts of possession Espanyol secured the victory with a third goal two minutes from time as Thievy Bifouma dispatched Manuel Lanzarote's cut-back.
Elsewhere, a superb solo goal from Cani clinched a 2-1 comeback victory for Villarreal over Valladolid.
Javi Guerra put Valladolid into the lead in the fourth minute when he scored in the corner after Zakarya Bergdich's piercing pass.
Villarreal fought hard for an equaliser and it came on 38 minutes as Giovani dos Santos stroked home his spot kick underneath the keeper's body after a foul from Gilberto Garcia on Jaume Costa in the box.
Both sides shared possession and chances throughout the second-half until Cani drove straight at the Valladolid defence in the 83rd minute and curled a finish into the top right corner with the outside of his foot to secure the three points for Villarreal.