Abel Resino's side secured a vital victory at Valladolid, while Valencia leapfrogged Real Sociedad with a valuable win at Mestalla thanks to a fine goal from Roberto Soldado
The visitors rose from the foot of the table to 18th with a well-deserved victory over Valladolid.
The win was only their third away from home in the league all season, and comes at a vital time with just one round of Liga games left this campaign.
Gustavo Cabral's header gave them the lead in the first half, before Iago Aspas stepped up and smashed a penalty into the net with his left foot to make it 2-0 after Marc Valiente was penalised for handling the ball inside the Valladolid box.
Celta are now just one point behind Deportivo in 17th after their defeat to Malaga.
BETIS 4-0 ZARAGOZA
Betis sealed a thumping win over Manolo Jimenez's side to consign the visitors to a nervous week ahead, as they dropped into the relegation zone with just one Liga round left to play.
Ruben Castro gave the hosts the best possible start when he opened the scoring in the first minute of the game, before Dorlan Pabon made it 2-0 with a smart finish 15 minutes later.
The Colombian attacker put in a sublime performance for the home side, as he supplied the assist to Jorge Molina for Betis' third before adding another himself with a well-taken strike in the 71st minute.
ATHLETIC 0-1 LEVANTE
Marcelo Bielsa's side ended their 100-year stay at San Mames with disappointment, as they were beaten 1-0 and had a man sent off against Levante.
The game was void of quality in the opening half as both teams struggled to construct decent passing moves, but it did spark to life after the break.
Iker Muniain came close to giving Bilbao the lead on the hour mark, before being shown a straight red just moments later for violent conduct.
Despite being a man light Bilbao continued to threaten, with Ibai Gomez the next player to come close to finding the net.
However, Juanlu popped up to break Bilbao hearts and steal all three points late in added time, as he hammered a shot past Gorka Iraizoz.
GETAFE 1-2 RAYO
A late own goal handed Rayo all three points after an entertaining game in Madrid.
The visitors started brightly, with Franco Vazquez, Alex Galvez and Roberto Trashorras all having chances to break the deadlock in the first half.
Despite their early dominance, Rayo went behind in the 48th minute when Rafa headed his side in front.
Chori Dominguez levelled things five minutes later, and after that the game looked to be heading for a draw, but deep in added time Diego Castro undid his side's good work by flicking the ball into his own net to gift Rayo the win.
VALENCIA 1-0 GRANADA
A vital win over Granada at Mestalla lifted Valencia into the Champions League places, as Real Sociedad dropped points at home to Real Madrid.
Roberto Soldado proved the difference as he instinctively met Joao Pereira's enticing cross from the right-hand side and diverted it past Roberto shortly before the hour mark.
Granada were unable to launch a comeback, though their Liga safety was confirmed for another year by Zaragoza's resounding loss to Betis.
OSASUNA 2-1 SEVILLA
An impressive display from the home team secured their Liga survival, as they edged past Sevilla in an entertaining game.
Osasuna posed the greater threat going forward in the first half, yet it was the away side that took the lead in the 50th minute when Jesus Navas set up Alvaro Negredo for an easy finish from close range.
The hosts did not take long to hit back though, as Francisco Punal made it 1-1 with a belting effort into the top corner from distance.
They then sealed their fine comeback in the 79th minute through Alvaro Cejudo. The midfielder sparked joyous celebrations from the Osasuna fans when he curled a low free kick past Beto.
MALAGA 3-1 DEPORTIVO
Manuel Pellegrini's side put in an accomplished performance to beat Deportivo 3-1 at La Rosaleda in their final home game of the season.
Javier Saviola gave them the lead on the brink of half-time, and Julio Baptista doubled the hosts' advantage with an emphatic effort midway through the second half.
Diogo Salomao reduced the deficit with a well-taken strike with 15 minutes left on the clock, but the impressive Isco put the result beyond doubt five minutes later with a very confident dribble and finish after being set up by a neat pass from Joaquin.
ATLETICO 0-0 MALLORCA
The shares were spoiled at the Calderon as neither side showed a clinical instinct in front of goal.
The result sends Mallorca to the foot of the Liga table, however, with results elsewhere going against them this weekend.
Radamel Falcao and Diego Costa wasted Atletico's best chances either side of half-time, while Giovani dos Santos came closest to scoring for the visitors when his well-struck shot was saved by Thibaut Courtois.