Goals from Maxi Gomez and Iago Aspas saw Celta Vigo beat La Liga champions Barcelona 2-0 at Balaidos on Saturday.
The result also means that Rayo Vallecano are relegated from La Liga after their 4-1 defeat at Levante earlier in the day.
Meanwhile, Atletico Madrid suffered a surprise 3-0 defeat at Espanyol. A Diego Godin own goal put the hosts ahead, before Borja Iglesias scored twice to seal the victory.
La Liga Results
Levante 4-1 Rayo Vallecano
Espanyol 3-0 Atletico Madrid
Alaves 0-1 Real Sociedad
Celta Vigo 2-0 Barcelona
La Liga Standings(Played, Goal Difference, Points)
1.