Real Sociedad seal Champions League place
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 Basque outfit finished fourth in La Liga despite defeat only thanks to Villarreal losing too.
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.
Celta Vigo lost 1-0 at Cadiz and are 17th, a point from safety, along with Almeria.
"To get to this situation we have done many things wrong, but I think sincerely, from the most self-critical position personally and as a group, that we don't deserve this in this way," Espanyol midfielder SergiDarder told Movistar.
"Above all, we want to say sorry. We have such a big club badge that in many moments, we haven't represented. I'm the first to be angry, but have no doubt we will be back."
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 European goal.
"I would have liked to be able to celebrate qualifying another way, but we have had a great season and are very happy," Real Sociedad striker Mikel Oyarzabal told Movistar.
"We have to celebrate, the fans should enjoy it, and next Sunday we can have a party at home, a celebration – we'll do all we can to win that game and end things well."
Victory leaves Atletico third, a point behind Real Madrid.
Villarreal will play in the Europa League next season, along with Real Betis, sixth, who beat Girona 2-1.
Osasuna, who fell to a late 2-1 defeat by Getafe which took the Madrid side two points clear of the relegation zone, are seventh and currently in line to qualify for the Conference League.
However Athletic Bilbao, Girona, Rayo and Sevilla remain in contention for the spot.
La Liga champions Barcelona enjoyed a series of emotional goodbyes in their final match at Camp Nou before the stadium is rebuilt, thrashing Real Mallorca 3-0.
Captain Sergio Busquets and defender Jordi Alba also played at home for the last time, in the club's penultimate league match of the season, and were awarded warm farewells by the sell-out crowd.
AnsuFati struck twice in the first half and Gavi added one after the break as the Catalans triumphed in style.
Marc-Andre terStegen earned his 26th clean sheet of the season, equalling the all-time record in the division, set by Deportivo La Coruna's Francisco Liano in the 1993-94 campaign.
The only bad news for Barcelona came when defender Alejandro Balde was taken off injured in the first half -- he will be out for at least six weeks and miss Spain's Nations League final four games in June.
Camp Nou, inaugurated in September 1957, has been one of football's most iconic stadiums since then.
Alba departed in tears when he was substituted in the final stages with the crowd chanting his name, while Busquets followed and was given an ovation of his own.
The duo could yet appear in Barcelona's final game of the season at Celta Vigo next weekend, but for nearly 90,000 supporters, this is the end of an era.
Busquets has won La Liga nine times and the Champions League on three occasions, making over 700 appearances for the club.
Alba departs with six La Liga trophies and one Champions League triumph among other silverware.
The duo both gave speeches on the pitch after the game.
"Since I was little I've dreamed of playing a game in this stadium that we're saying goodbye to temporarily," said Busquets.
"We're already the best club in the world, with the best players, and now we'll have a stadium on that level."