The Colombian striker netted in the second half to give Diego Simeone's men a narrow win over Sevilla, meanwhile there was vital wins for Valencia and Espanyol
Mallorca provisionally moved up to third-bottom in the Spanish Primera Division with a tight 1-1 draw with Rayo Vallecano on Friday night.
They didn't get off to the best of starts though. Jose Casado burst down the left-hand side and clipped a ball into the box for Piti, who adjusted his body to spectacularly volley into the bottom right corner with his left-foot.
However, the Madrid-based side were pegged back by the Islanders five minutes later. A corner kick came in from the left and Alejandro Alfaro came out best in a goalmouth scramble to stab home from a couple of yards out.
The rest of the match saw goalkeepers, Juan Calatayud and Ruben solidly keeping the match all square with a string of decent saves, but Rayo passed up the best opportunity to steal all three points.
Jordi Figueras slipped a pass through to Lass Bangoura and the Guinean smashed an effort of the left-hand post, leaving the honours even as the full time whistle blew.
GRANADA 1-1 VALLADOLID
Granada lifted themselves out of the relegation zone by coming from behind to earn a 1-1 draw with Valladolid at Los Carmenes.
The hosts were coming off heavy defeats from Atletico Madrid and Real Betis, but seemed eager to make amends as they started the match with intensity.
Youssef El Arabi and Nolito had decent chances to open the scoring in the first period, but they found themselves up against an in-form Jaime Jimenez in the Valladolid goal.
The deadlock was eventually broken against the run of play 58 minutes in when Patrick Ebert smashed a 30 yard free kick into the top bag.
Odion Ighalo saw a strike ruled out for offside, but Granada wouldn't have long to wait to equalise.
Substitute Diego Buonanotte curled a cross in to El Arabi who cushioned a header into the bottom corner to finally get the better of Jaime in the Valladolid goal.
Lucas Alcaraz's men probed for the winner in the latter stages but ended up having to settle for a point in the end.
VALENCIA 5-1 MALAGA
Valencia moved three points clear of Malaga in the Primera Division with a comprehensive 5-1 victory over Manuel Pellegrini's outfit on Saturday evening.
A largely uneventful opening 25 minutes burst into life when the hosts went on a goalscoring blitz before the half-time.
Dani Parejo got the ball rolling when he took advantage of some unsure defending at the back to get in behind the Malaga back-line to slot home.
The next goal came from some magnificent work down the left wing by Aly Cissokho. The Senegalese went on a marauding run and left Jesus Gamez and Manuel Iturra for dead before lashing a cross to the back post, where Roberto Soldado easily slotted home.
Los Che made it three goals in five minutes when Ever Banega was tripped in the box by Martin Demichelis and Soldado netted the resulting penalty to grab his second of the game.
Astonishingly, Valencia made it 4-0 just 11 seconds after the kick-off from the previous goal when they pressed the Malaga defenders relentlessly before Sergio Canales latched on to a save from Willy Caballero to pass into the empty net.
The visitors were shells-shocked, but still clawed a goal back just before the break when Julio Baptista scored with a superb free kick, but the damage had been done in the opening 31 minutes.
The icing on the cake for Ernesto Valverde's men came 10 minutes into the second half when Banega cut inside from the left and rifled a strike into the roof of the net.
Malaga solidified themselves for the rest of the match, but were unable to mount even a glimmer of an unlikely comeback.
GETAFE 0-2 ESPANYOL
Getafe's European hopes were dealt a blow on Sunday morning as they lost 2-0 at home to a resurgent Espanyol side.
Paco Alcacer went through on goal only to be denied by goalkeeper Cristian Alvarez in what was the only chance of a largely tepid opening.
The opening goal eventually came through a superb team move from the Barcelona-based side. Joan Verdy started the move with a pass out to Christian Stuani, who stood a cross up to the back post for Sergio Garcia. The 29-year-old nodded the ball down to Verdu, who continued his run into the box to finish off the move with an accomplished finish.
The task became near-impossible in the second half when Borja Fernandez and Federico Fernandez both received their second yellow cards for an inexplicable handball and a needless barge.
To make matters worse, the resulting free kick from Mubarak Wakaso was finished from close range by Stuani to make it 2-0.
Nine-man Getafe never looked like getting back into it, and now find their Europa League ambitions distancing.
DEPORTIVO 1-1 ATHLETIC BILBAO
In-form Deportivo saw their renaissance halted by Athletic Bilbao as Fernando Llorente scored his first league goal since September to earn a 1-1 draw for Marcelo Bielsa's side at the Riazor.
Fernando Vazquez had guided his side to four consecutive victories in La Liga, and they looked likely to continue the run 38 minuted in Bruno Gama opened the scoring.
The former Porto man picked up the ball on the edge of the area and crashed a fantastic strike into the roof of the net past Gorka Iraizoz.
Llorente looked up for the battle, though, and showed shades of his form from last season six minutes later when he out-jumped the Depor defence to head home from Andoni Iraola's cross.
The Juventus-bound striker and Markel Susaeta both saw attempts come off the woodwork in the second half, but their ascendancy was halted when Ander Iturraspe was shown his second yellow card for a foul on Gama.
The hosts could not make the most of their numerical advantage and both sides ended up having to settle for a point.
OSASUNA 0-0 REAL SOCIEDAD
Real Sociedad failed to maintain the gap between themselves and Valencia in the Primera Division as Philippe Montanier's men could only manage a 0-0 draw away to league strugglers Osasuna.
The majority of the match was bereft of out-and-out goalscoring chances, but it was the visitors who looked more likely.
Antoine Griezmann and Emiliano Armenteros had opportunities early on but neither could find the net against their opposition goalkeepers.
In the second half Xabi Prieto came closest to opening the scoring with a shot from the edge of the area, but Andres Fernandez done well to turn the attempt round the post.
Both goalkeepers were in decent form throughout the match but, in the end, neither side looked like to grab a goal and claim all three points.
SEVILLA 0-1 ATLETICO
A solitary strike from Radamel Falcao was enough for Atletico Madrid to stay just three points behind rivals Real Madrid in La Liga as Diego Simeone's men ran out narrow 1-0 winners over Sevilla at the Ramon Sanchez Pizjuan.
Los Colchoneros were largely frustrated by Unai Emery's outfit for the majority of the match but the vital goal of the game came 12 minutes from time through Falcao.
Raul Garcia tried his luck with a volley from the edge of the penalty area by the predatory Colombian striker stuck out a leg to turn the ball into the net past Antonio Beto.
It looked like the visitors were comfortably going to see out the victory but they were given a late scare in the dying minutes.
Ivan Rakitic crashed a free kick off the crossbar in injury-time, ensuring Atletico maintain the pressure on Jose Mourinho's men in second place in the league.
CELTA VIGO 2-1 REAL ZARAGOZA
Mario Barmejo fired home a stoppage-time winner as Celta Vigo fought from a goal down to beat Real Zaragoza 2-1 in a crucial relegation clash on Monday.
Abel Resino's men had begun the evening at the foot of the Liga standings and were minutes away from remaining there until Barmejo struck in the 93rd minute to breathe fresh life into their fight for survival.
The hosts looked to have given themselves a mountain to climb after going behind to a Cristian Sapunaru header in the 26th minute.
Zaragoza's lead was shortlived when Alex Lopez rose highest to nod the hosts level some 10 minutes later after a good cross from Augusto Fernandez.
Both sides struggled to forge the goalscoring opportunities needed and, with little time remaining, it seemed that each side would have to settle for a point. Mario Barmejo, however, had other ideas.
Fabian Orellana picked out Barmejo in the centre of the area, and the 34-year-old swivelled and fired left-footed into the bottom corner of the goal beyond Roberto Gago.
The Blanquillios now move off the bottom of the standings at the expense of Zaragoza and continue their push for safety with a visit to Levante on Saturday.