The home side were ahead after 16 minutes when Alejandro Alfaro tapped home from close range, with that score still standing at the interval.
Sevilla were level just past the hour mark when Alvaro Negredo slotted into the back of the net from inside the box. However, Mallorca regained the lead moments later when Alfaro scored his second of the match.
The away side pushed for the leveller in the latter stages, but they could not make the breakthrough as Mallorca held on for a vital three points in their fight for survival.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
MALLORCA: Aouate; Hutton, Nunes, Kevin, Bigas; Tissone, Marti, Pina, Victor; Alfaro, Giovani
SEVILLA: Beto; Navarro, Fazio, Coke, Botia; Moreno, Navas, Rakitic, Medel, Kondogbia; Negredo