The islanders won for the 11th time in 12 home games thanks to goals from Julio Alvarez, Victor and Pierre Webo (pictured) as they joined fourth-placed Sevilla on 43 points.
Mallorca are fifth due to their inferior head-to-head record with Manolo Jimenez's side.
"We'll continue to fight for a place in Europe and if a team in the Champions League slots (top four) fades or loses their consistency we could have a chance," Mallorca coach Gregorio Manzano told reporters.
Real Madrid replaced Barcelona at the top on Saturday after beating Sevilla 3-2 thanks to a stirring comeback.
They drew level on 62 points with Barca, who were held 2-2 in Almeria, but moved above the champions through their superior goal difference.
Valencia are third with 46 points and can strengthen their position with a win at home to Racing Santander on Monday.
Gaizka Toquero scored twice for Athletic Bilbao in a 2-0 home win over Real Valladolid and are seventh with 40 points.
In other games on Sunday, basement side Xerez rallied from 2-1 down to register their first away win in La Liga with a 4-2 victory in Malaga.
Both sides finished with 10 men but a double from Momo (one a penalty) and strikes from Leandro Gioda and Fabian Orellana delivered the points for the top-flight debutants.
Xerez stay bottom with 15 points from 25 games, 10 adrift of safety.
Real Zaragoza, in 17th spot, let slip a one-goal lead to draw 1-1 at home to Atletico Madrid.
Jiri Jarosik headed Zaragoza in front from a seventh-minute corner and Atletico's Jose Antonio Reyes was sent off midway through the second half.
King's Cup finalists Atletico threw on substitute Ibrahima Balde in the closing stages and the youngster headed the equaliser in stoppage time.
Espanyol drew 0-0 with Villarreal, as did Osasuna with Getafe.
