Late goals from John Guidetti and Hugo Mallo gave Celta Vigo a 2-0 win at hapless Valencia to pile more misery on coach Gary Neville, who was the subject of angry chants by the Mestalla crowd.
The Galicians made the most of Athletic Bilbao's 2-1 defeat to Espanyol earlier on Sunday to move above the Basques and into the top six, boosting their chances of playing European football next season.
Valencia, meanwhile, were dealt a further blow after exiting the Europa League on away goals on Thursday and lie 14th in the Primera Division table, six points off the relegation zone.
Valencia were fortunate to make it to half-time without conceding as the Galicians created a series of clear-cut chances.
Goalkeeper Mat Ryan had to scramble the ball off his line after Shkrodan Mustafi deflected a cross off the near post, and the Australia international had to make further saves to deny Guidetti and Daniel Wass.
Valencia improved in the second half but fell behind after 80 minutes as Guidetti latched onto an audacious back-heel by Fabian Orellana to lash home.
Five minutes later captain Mallo finished off the hosts, coasting down the right-hand side and cutting inside to beat goalkeeper Ryan at the near post.
Valencia could have conceded again before the final whistle sounded.
Orellana's attempted chip went just wide of the near post, and then the Chilean struck the woodwork with the goal gaping.
As the whistle approached, furious Valencia fans turned their anger on Neville, chanting "Gary go now".