The big moment in the match arrived on the hour mark as Alcacer converted from a corner to break the deadlock, before returning defender Mathieu put into his own net at full stretch at the very end
Victory for Barca ends a two-match winless run in European competition without scoring and also saw them strengthen their grip on top spot, which they were under no risk of relinquishing on the final matchday.
Home boss Ernesto Valverde made eight changes to his side on the back of the 2-2 draw against Celta Vigo at the weekend, compared to four for the visitors - star men Bas Dost, Gelson Martins and Fabio Coentrao all surprisingly being left out.
Barcelona struggled to make too many chances in the first half, however, with their best opening falling the way of Suarez, who was denied by Rui Patricio from close range.
Suarez was then wasteful with a shot from distance, as was returning midfielder Andre Gomes, while Bruno Fernandes's speculative attempt at the other end of the pitch was easily dealt with by Jasper Cillessen.
Sporting, seemingly more focused on domestic matters having already assured third spot in Group D prior to this fixture, were boosted for the second half by the introduction of Martins and top scorer Bas Dost.
Martins almost instantly gave the Lions something a little different, running at the Barca defence - consisting of their only two fit centre-halves in Gerard Pique and Thomas Vermaelen - before dragging the ball wide.
A subdued Camp Nou finally had something to cheer on the hour mark when Alcacer got ahead of his man and glanced the ball into the far corner of the net.
Sporting created their best opening of the match moments later, with Bas Dost failing to make it nine goals in 10 games by somehow picking out compatriot Cillessen in the middle of the goal from six yards out.
A first win on Spanish soil in 12 attempts always looked likely to evade Sporting, though, as they shut out the opposition for large parts but struggled to get the ball forward too often.
Bas Dost did have another opportunity to snatch a point, only to volley wide unmarked inside the box, while Messi saw a curler pushed aside by Patricio late on.
Barca, now unbeaten in 24 European home matches since September 2013, did manage to double their tally in added time through Mathieu, who turned Denis Suarez's cross into his own net at full strength.
Barcelona (4-3-3): Cillessen; Semedo, Vermaelen, Pique (Busquets 64'), Digne; Rakitic, Gomes, D.Suarez; L.Suarez (Paulinho 75'), Alcacer, Vidal (Messi 61')
Sporting Lisbon(4-2-3-1): Patricio; Piccini, Coates, Mathieu, Bruno Cesar (Coentrao 64'); Battaglia, Carvalho; Ristovski (Martins 46'), Fernandes, Acuna; Ruiz (Bas Dost 46')