Alcacer, named in a league starting XI by Ernesto Valverde for the first time since the opening match of the season, scored once in each half as Barca restored their four-point lead at the top of the table after wins for title rivals Valencia and Atletico Madrid earlier on Saturday.
Guido Pizarro's headed equaliser in between Alcacer's two strikes briefly threatened a surprise result, but a draw would have flattered fifth-placed Sevilla, who have now lost four consecutive away games.