Carlos Bacca, Daniel Carrico and Kevin Gameiro all scored for Sevilla with Aleix Vidal claiming a late consolation for the home side as the result kept the pressure on sixth-placed Real Sociedad, who are two points clear of Sevilla in the overall standings.
The scoreline also left struggling Almeria in the bottom three but only one point from safety in a congested bottom half of the table.
Sevilla started on the front foot with both Carrico and Gameiro on target and forcing saves from Almeria goalkeeper Esteban Suarez in the early exchanges, with Jose Antonio Reyes also posing a threat with a couple of testing corners.
The deadlock was finally broken in the 31st minute when Bacca slotted in from Gameiro's cross from the left.
Sevilla then doubled their lead from a set piece seven minutes after the break when Carrico was in the right place to poke in a Reyes corner.
Suso almost pulled one back immediately for Almeria but goalkeeper Antonio Beto parried his effort to safety before he comfortably caught headers from Jose Antonio Verza and Helder Barbosa as the home side went on the attack.
Gameiro then put the game beyond Almeria with a 77th-minute close range score before Vicente Iborra's shot rattled the post, but the home side hit back with a late consolation through Vidal, who fired in Jonathan Zongo's assist from the left of the area.