The Islanders called new names Fernando Tissone and Alan Hutton into their starting XI, while Antonio Lopez returned on the bench, but they failed to provide any inspiration as Mallorca instead lost ground in their survival fight.
Javi Marquez's dismissal on the half-hour, following two cautions in the space of four minutes, paved the way for Sociedad to surge to victory after half-time with goals from Gonzalo Castro, Carlos Vela and Diego Irfan.
Mallorca have now won just once in 17 league games and are four points adrift of safety.
Sociedad, who beat Barcelona 3-2 last time out at the Anoeta, are by contrast entrenched in the top half of the Primera Liga table following a seven-game unbeaten run at home.
The hosts controlled the first period and, while they failed to convert that on to the scoreboard, they at least had a man advantage to show for it.
Mallorca goalkeeper Juan Calatayud had been busy in the opening 30 minutes, saving from Vela and a close-range Antoine Griezmann header, before Marquez was given his marching orders.
The midfielder was first booked for a foul on Castro after 26 minutes and moments later the referee was left with no option but to show a red card after whistling for handball.
Griezmann tested Calatayud with another header shortly after and, while the short-handed Mallorca resistence made it to half-time, they failed to hold out much longer after the restart.
Castro made the initial breakthrough on 55 minutes. An over-worked Calatayud had initially blocked Vela's shot from six yards before Castro side-footed in from the same distance.
Mallorca boss Joaquin Caparros responded by sending on Lopez for his return after three months out with a knee injury.
Lopez had this week vowed to "make war" in a bid to try and revive his side and his team-mates initially responded to his presence by forging their first real chance - skipper Jose Nunes forcing goalkeeper Claudio Bravo into saving his header.
It was a short-lived moment of promise as Sociedad went 2-0 up on 70 minutes through Vela, as he latched on to Ruben Pardo's assist to score from 12 yards.
Castro and Imanol Agirretxe both shot narrowly wide before Irfan sealed the result two minutes from the end.
Agirretxe fed a pass to the substitute for him to score low into the right corner from 12 yards.
