Ronaldo Koeman went with Ousmane Dembele, Ansu Fati, captain Lionel Messi and Antoine Griezmann in a front-four following last Saturday's EL Clasico defeat.
Fati should've given Barcelona the lead in the first 12 minutes from a ball on the near side of the area, but the youngster dragged the inviting opportunity wide of the mark.
Alaves threatened minutes later when a through ball from the middle released a surging Deyverson down the right who brought Neto to a low save off a close-range strike.
The Catalans regained momentum before the half-hour mark and witnessed a free-kick from Messi cleared from the goal-line with Sergio Busquets fluffing the follow-up.
Barcelona were behind on 31 minutes when Luis Rioja caught Neto in sixes and sevens following a back-pass from Gerard Pique to prod into an empty net.
An injury for the hosts forced their hand four minutes before halftime after Ximo Navarro made way for Martin Aguirregabiria.
Koeman's side went close to level matters following the start of the second period, as Fati volleyed wide from the far side after getting on the end of Sergi Roberto's cross.
Alaves were down to ten players on 62 minutes when Jota was sent packing for catching Pique in the chest with a high boot, thus seeing a second yellow card.
The Catalans took advantage of the situation under a minute after a loose ball outside the area fell straight to Griezmann, who went and chipped into the bottom-corner.
Barca had their tails up towards the closing period, and had Messi placing in a low curler in the area, but Fernando Pacheco palmed for a corner-kick.
Blaugrana enjoyed more openings in the last seconds with shots from Sergio Dest and Miralem Pjanic bringing Pacheco to work while Messi fired wide, as it finished all square.
