Leo Suarez and Dani Rodriguez did the damage in the first leg for Vicente Moreno's men and, although Jeremie Bela made the tie interesting in Albacete, Mallorca just about did enough to cling on.
Bela opened the scoring with 16 minutes on the clock with a fine free-kick from just outside the area, filling the host with belief.
But it struggled to really control proceedings, as Mallorca offered plenty of attacking threat itself.
Albacete piled the pressure on in the final stages, with Roman Zozulya heading wide from close range, but their efforts came to nothing.
Mallorca – which was only promoted from Segunda B last season – will face Deportivo at the Riazor in the first leg, before hosting Jose Luis Marti's side at Son Moix three days later.
Success over the two legs will see them return to the top flight for the first time since 2012-2013.