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.
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.
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.
