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.
Barca have won 10 and drawn one of their first 11 league games and now sit 11 points clear of rivals Real Madrid, who are at home to Las Palmas on Sunday, in fourth.
Sevilla have now failed to win in 15 attempts at Camp Nou, losing 13 of those meetings and conceding 40 goals in the process.
Barcelona came close to an opener on multiple occasions in a frantic opening 10 minutes.
Lionel Messi, on his 600th Barca appearance, created an early effort for himself which was saved by David Soria, before Sergio Busquets' close-range effort was hacked away off the line by Sevilla's defence after the Argentina international crossed into his path.
Luis Suarez then failed to lob Soria after a fine pass from Andres Iniesta and Ivan Rakitic sent a blistering left-footed 20-yard drive inches wide.
Luis Muriel briefly interrupted the flow of Barca attacks, firing narrowly off target at the other end after dispossessing Samuel Umtiti, but Iniesta's left-footed thunderbolt - which was similar to Rakitic's - soon had Soria worried again.
The lively Alcacer headed just over from Rakitic's cross, but the striker made no mistake with his next chance on 23 minutes.
Taking advantage of a mistake from Sevilla captain Sergio Escudero, whose poor touch failed to deal with Suarez's throughball, Alcacer raced in on goal to slide a first-time finish past the onrushing Soria from 15 yards.
Sevilla improved after the break and saw Muriel's shot from 18 yards only just clear Marc-Andre ter Stegen's crossbar, and the visitors did find an equaliser shortly before the hour mark.
Pizarro latched on to Ever Banega's corner and his downward header from eight yards bounced past Ter Stegen and into the top corner.
That seemed to wake Barca from their sluggish start to the second half and Gerard Pique almost sent the Camp Nou crowd wild when he fired an effort against the bar from 25 yards.
Barca moved back in front just six minutes after the equaliser, Alcacer timing his run to prod Rakitic's deflected cross past Soria from six yards.
Alcacer was immediately substituted for Gerard Deulofeu after his second goal, but Barca were back on the attack soon after and Suarez wanted handball against Clement Lenglet when his shot struck the Sevilla defender's arm from close range, the striker having been found by Messi.
Barca had another penalty claim turned down when Rakitic raced into the area and was felled under pressure from Escudero late on, but it mattered little with Sevilla not threatening a second leveller as Valverde's side reached the international break in a dominant domestic position.
