The hosts secured what could be a crucial victory in their quest for survival against high-flying Sociedad, but were forced to do things the hard way after Carlos Vela opened the scoring early on.
Vela coolly slotted home past Esteban from the spot after 21 minutes when Angel Trujillo handled in the area, only for Almeria to hit back before the break through a delightful finish from Oscar Diaz.
After he got on the end of a lofted ball, with Claudio Bravo off his line, Diaz chipped the onrushing goalkeeper to level the scores.
Imanol Agirretxe produced a sublime chip of his own early in the second half when he lobbed Diaz's opposite number Esteban to restore the visitors' lead.
Still the goals continued as Verza tucked away the second spot kick of the game after Aleix Vidal was adjudged by the referee to have been brought down inside the area by Carlos Martinez.
Sociedad then saw Agirretxe's effort cleared off the line before Mikel Gonzalez felled Vidal in the area, with Verza again keeping calm to edge the hosts ahead.
It looked as though Almeria would be denied the three points when Markel Bergara headed home five minutes from time before an attempted clearance struck Hicham Khaloua and rebounded past Bravo in the visiting goal.
