With seven matches remaining and four berths in Europe's elite club competition up for grabs, Mallorca are fifth, below Sevilla, who won 2-1 at Malaga on Saturday, due to an inferior head-to-head record.
Defeat for third-placed Valencia shrinks their lead over the chasing pair to five points and they are a massive 21 behind Real Madrid, who lost 2-0 at home to champions Barcelona on Saturday to surrender top spot to their arch rivals.
NEWS:Barca beat Real at Bernabeu
Mallorca were seen as likely candidates for relegation due to their financial difficulties but the Balearic Islanders have defied expectations and have now won 13 of their 15 home matches this season.
Gonzalo Castro set them on their way in only the sixth minute at a half-empty Ono Estadi with a deflected strike that Cesar Sanchez could only parry into the net.
Cameroon striker Pierre Webo doubled the home side's lead with a superb diving header in the 21st and Jordi Alba pulled a goal back for the visitors just after the break.
Valencia's Portuguese midfielder Manuel Fernandes had a torrid time filling in at centre back after an injury to Hedwiges Maduro and his attempted clearance flew into the roof of his own net in the 63rd.
Mallorca looked to be cruising before Pablo Hernandez slipped the ball under Mallorca goalkeeper Dudu Aouate with four minutes remaining and Fernandes's night went from bad to worse when he clashed with Aritz Aduriz shortly after and was shown a straight red card.
Athletic Bilbao pressed their claim for a European place when they trounced Almeria 4-1 earlier on Sunday to climb to sixth, the second of Spain's two Europa League spots, on 48 points.
Javi Martinez scored either side of half time, Fernando Llorente netted one and had a penalty saved and Igor Gabilondo was also on target before Pablo Piatti grabbed a late consolation goal for visiting Almeria.
Europa League semi-finalists Atletico Madrid stay in 10th after they suffered a 3-0 drubbing at Espanyol and had Czech defender Tomas Ujfalusi sent off late on for a wild lunge on Juan Forlin.
Racing Santander moved six points clear of the relegation places after a 1-1 draw at mid-table Deportivo La Coruna and are 15th on 32 points, above Real Zaragoza (32) and Malaga (31).
Promoted Tenerife (26) and Real Valladolid (25), who drew 0-0 on Saturday in Valladolid coach Javier Clemente's first match in charge, are 18th and 19th respectively.
Xerez (23), making their La Liga debut, are bottom after Saturday's 1-0 home defeat by Getafe.
