Real Sociedad fell to a 2-1 defeat at Atletico Madrid on Sunday but still sealed qualification for next season's Champions League after Villarreal were beaten 2-1 at Rayo Vallecano.
Imanol Alguacil's side reached Europe's premier competition for the first time since 2013 as the Yellow Submarine's slip-up at Vallecas ensured the Basque club finish fourth.
Espanyol were relegated from the top flight after Valencia's Samuel Lino struck a stoppage time equaliser in a gripping 2-2 draw.
One other side will go down along with already-relegated Elche on the final day of the season, with Real Valladolid currently 18th, a point from safety, after they drew 0-0 at Almeria.
Antoine Griezmann and Nahuel Molina struck for Atletico in their win over Real Sociedad, who struggled to create much of note, perhaps aware of Villarreal's struggles.
Eventually Alexander Sorloth pulled one back for the visitors at the Metropolitano to give them something to celebrate as they achieved their goal.
Victory leaves Atletico third, a point behind Real Madrid.
Raul de Tomas and Isi Palazon netted for Rayo against Quique Setien's side, who pulled a late goal back through Giovani Lo Celso, but could not turn the game around.
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