Atletico Madrid solidified their place at the top of the table with 1-0 over Granada, while Real Madrid lost 2-1 at Sevilla.
Real's controversial 4-3 Clasico loss to arch rivals Barcelona at the Bernabeu on Sunday saw them replaced by Atletico at the table's summit and they were unable to bounce back from that defeat.
Cristiano Ronaldo gave them a 14th-minute lead at Estadio Ramon Sanchez Pizjuan, but the deficit was overturned just a few moments later as Carlos Bacca poked the ball past Diego Lopez.
The visitors enjoyed more of the ball than their hosts in the second half, but Bacca's contribution was vital - as he netted his second with 18 minutes left to give Sevilla all three points.
The victory was Sevilla's sixth consecutive triumph in the league, moving them to within six points of fourth-placed Athletic Bilbao, while Real slip three points behind leaders Atletico, who won without playing particularly well.
Atleti struggled to break through Granada in a frustrating first half, but top scorer Diego Costa salvaged all three points after 63 minutes with his 24th Liga goal of the campaign.
Real's defeat means Atleti are a point clear of Barcelona as the title race swings between three teams.
Barcelona moved up to second, above Real, thanks to their 3-0 home win over Celta Vigo, but the victory was marred by a season-ending knee injury to goalkeeper Valdes.
The goalkeeper has already announced his intention to leave at the end of the campaign, meaning that he has played his final game in a Barcelona shirt.
He suffered a torn anterior cruciate ligament after landing awkwardly while collecting a routine ball into the box, and he is now set for surgery that also puts his FIFA World Cup participation with Spain in doubt.
Away from that incident, two goals from Neymar and one from Lionel Messi was more than enough to see off a Celta side coached by Barca legend Luis Enrique.
The day's other game saw Rayo Vallecano take a big leap towards survival as they beat another of the league's relegation contenders, Osasuna, 1-0 at home.
Rayo went into the match a point above their visitors and it looked set to end all-square at Estadio de Vallecas as proceedings entered second-half stoppage time with the scores level.
However, Jose Carlos won a late penalty after a tug from full-back Damia and forward Joaquin Larrivey converted the resulting spot-kick to win it.
