Marcelo Bielsa's men came back from behind to gain all three points against relegation-threatened Zaragoza, while there were wins for Valencia, Sociedad, and Granada
Valencia maintained the pressure on fourth-placed Real Sociedad with a narrow 1-0 victory over Getafe at Coliseum Alfonso Perez.
A win for los Che would have seen them provisionally move into the Champions League places, and they started the match with intent and impetus, as Roberto Soldado headed just over the bar from an Andres Guardado cross in the early stages.
It looked as if it would be all square entering the break, but Jeremy Mathieu broke the deadlock when he received a pass from Ever Banega and coolly slotted into the far corner from the edge of the area.
Ernesto Valverde's men dominated the second period, but failed to register another goal as they came up against an in-form Miguel Moya. The Getafe keeper kept his side in with a shout with a string of saves to deny Soldado, Jonas, and Mathieu.
In the end, one goal was enough for Valencia to record their third consecutive Liga win.
GRANADA 3-0 OSASUNA
Granada's survival hopes were given a massive boost on Saturday as they came out comfortable 3-0 winners over Osasuna at Los Carmenes.
The home side came out swinging from the start, clearly desperate to maintain their Liga status for next year. Emiliano Armenteros and Diego Mainz had opportunities within the first two minutes, but both sent their headers wayward.
They eventually took the lead 23 minutes in when Guilherme Siqueira whipped a cross along the box for Youssef El Arabi to place home.
Osasuna grew into it as the game progressed, but any hopes they had of equalising were dashed 10 minutes from time when Nano brought down El Arabi as the last man inside the box and was subsequently sent off. Siqueira dispatched the resulting penalty with a cheeky dink down the middle.
The points were wrapped up for Granada in injury time when Buonanotte cut in from the right-hand side and finished from the edge of the box.
SEVILLA 1-2 REAL SOCIEDAD
Real Sociedad's pursuit of Champions League football is still in their own hands as Philippe Montanier's men fought back from a goal behind to earn a crucial 2-1 win over Sevilla on Saturday evening.
Valencia's win over Getafe earlier in the day ensured the pressure was on for the visitors as they travelled to the Ramon Sanchez Pizjuan, and they didn't get off to the best of starts.
Ivan Rakitic gave los Nervionenses the lead 10 minutes in when Geoffrey Kondogbia received the ball from a short corner and placed a pass inside to the Croatian, who finished into the bottom left corner from just outside the six-yard box.
However, Rakitic would go from hero to zero six minutes later when he headed into his own goal to make it 1-1.
Sociedad turned the game on its head eight minutes later when Carlos Martinez cut in from the right and floated a cross to the front post, where Imanol Agirretxe volleyed into the right corner.
Controversy occurred around the hour mark. The linesman flagged a Sevilla goal as offside and Jose Antonio Reyes was sent off for his complaints, despite being a substitute on the side of the park.
Papa Diawara headed over the bar in the latter stages as Sevilla pushed for an equaliser, but Sociedad held on for the all-important three points.
LEVANTE 2-3 RAYO
Rayo moved up to eighth place in the Primera Division with a 3-2 win over Levante in an entertaining clash at Ciudad de Valencia on Sunday afternoon.
The visitors struck first 20 minutes in when Chori Dominguez's free kick was palmed back into play by goalkeeper Keylor Navas. Piti showed his predatory instinct to latch on to the rebound and smash home for his 16th of the season.
Levante came out of the blocks quickly after the break, though, and equalised after seven minutes. The Rayo defence was static as they called for an offside, but the ball fell to Ruben Garcia who crossed for Robert Acquafresca to finish.
However, the Madrid-based side quickly restored their lead. A pacey counterattack eventually saw Navas parry Piti's strike towards goal, allowing Franco Vazquez to tuck home from the save.
Rayo must have thought they had wrapped up the points when Chori was fouled inside the area and Piti doubled his tally for the day by scoring the resulting penalty.
A grandstand finish looked to be in store when Vicente Iborra netted with a powerful header to make it 3-2, but Rayo got over the line in the end to claim the win.
DEPORTIVO 2-0 ESPANYOL
Deportivo were given a boost in their quest to avoid relegation with a vital 2-0 home win over Espanyol on Sunday afternoon.
It was Javier Aguirre's side who started brightly, though. They could have taken the lead after just two minutes when Christian Stuani bounced a header off the crossbar.
Both sides exchanged chances in the first half, but it would be Depor who struck the first just after the break. Bruno Gama picked up possession on the edge of the box and whipped a cracking strike into the bottom corner.
The goal settled down the home side, as they looked relatively comfortable in the second half.
The three points were wrapped up for Deportivo in the dying minutes when Nelson Oliveira terrifically lobbed Cristian Stuani from the edge of the area.
ZARAGOZA 1-2 ATHLETIC
Real Zaragoza slipped back into the relegation zone after a late rally from Athletic Bilbao saw the Basque side run out 2-1 winners at La Romareda.
Marcelo Bielsa's men were also hoping to secure Liga football next season with a point on Sunday, but fell behind early doors after a goal from Helder Postiga, as the Portuguese rose highest in the box to head home after a great cross from Paco Montanes.
Gorka Iraizoz kept his side in it shortly after the break when he denied the former Tottenham player from close range.
It took Athletic a long time to get going, but they eventually got their equalising goal with 10 minutes remaining when Fernando Llorente took advantage of a scramble inside the box to finish from a yard out.
The honours looked certain to remain even, but Ibai Gomez popped up in injury time to back-heel in from the edge of the six yard box, ensuring Athletic maintained their record of having never been relegated from the top flight.