Athletic Bilbao and Malaga won in the Primera Liga on Saturday, while Getafe salvaged a point against Osasuna and Granada drew with Real Sociedad.
Malaga cemented their fourth position in the table with a 2-0 win at 10-men Sevilla in the late kick-off.
Martin Demichelis put the visitors ahead four minutes after the re-start and Sevilla's night then got worse when Federico Fazio was sent-off - and conceded a penalty - for a professional foul.
Eliseu converted the subsequent spot-kick in the 70th minute to seal the points for Malaga.
Aritz Aduriz's 11th-minute header consigned Real Mallorca to their ninth defeat in 11 league games, but Athletic Bilbao were just as thankful to goalkeeper Gorka Iraizoz for the three points as they moved nine points clear of the relegation zone.
The visitors went in front with their first serious attack as Andoni Iraola's searching cross found Aduriz free at the back post to head home his 11th goal of the campaign.
Mallorca then created countless opportunities to get back in the game but Iraizoz was equal to efforts from Giovani Dos Santos, Tomer Hemed and Victor Casadesus before the break, whilst Victor also fired wide with an open goal after the interval.
Another defeat means that Mallorca's winless streak extends to 14 games in all competitions.
Diego Castro's penalty deep into stoppage time salvaged a point for Getafe against Osasuna in a game desperately lacking in quality at the Alfonso Perez Coliseum.
Both sides had one great opportunity to take the lead in the first half but neither Nino nor Alvaro Vazquez could convert when clean through on goal, and the game only came to life after Emiliano Armenteros had been sent off for the visitors 12 minutes from time for a wild lunge on Juan Valera.
However, despite losing a man, Jose Mendilibar's men seemed set for all three points when Kike Sola weaved a way through the Getafe defence to slot home six minutes from time.
However, Osasuna were cruelly denied a second away win of the campaign in the final minute of added time as Oier was harshly adjudged to have handled inside the area and Castro stroked home his fourth goal of the season.
Granada claimed a share of the spoils at home to Real Sociedad but failed to score for the fifth successive league game.
In a match of precious few chances at the Estadio Nuevo Los Carmenas, the hosts bounced back from shipping four against Malaga last weekend and moved out of the relegation zone on goal difference after the stalemate.