The Spain striker shot home neatly on 23 and 65 minutes, with Guido Pizarro levelling temporarily for Sevilla with a stunning header.
Barca were comfortably on top before the break but Sevilla bossed the early stages of the second half.
Ernesto Valverde's men. though, looked slick once more once Alcacer rounded off a clinical move that peaked with Messi's clever pass out to the right and Ivan Rakitic's precision cross.
Former Valencia star Alcacer now has nine goals in nine starts this term.
And his razor-sharp instincts were the decisive factor against a Sevilla side who showed increasing confidence in the 20 minutes before's Alcacer's clincher. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇
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