The Catalan giants added to their 3-0 first-leg victory in Basque Country at the end of October to run up a 6-1 aggregate scoreline, though they were given an early scare by the visitors when Viguera pounced on a defensive mix-up to open the scoring after 17 minutes.
However, Adriano, who was at fault for the first goal, restored parity shortly after the half-hour mark. The Blaugrana took control in the second half, surging into the lead thanks to a sublime free kick from David Villa, who added a third goal almost instantly after from a sweeping break.
Barca now awaits its opponents in the fifth round, with the first leg set to take place on Dec. 11-13, but must first turn attentions to their Liga clash against Athletic Bilbao on Saturday.
Tito Villanova opted to exclude a host of his regulars in his starting XI, with familiar faces such as Villa and Javier Mascherano lining up alongside the likes of Sergi Roberto and Jonathan Dos Santos.
Facing a three goal deficit, Alaves nonetheless threatened to make a contest out of the tie when it stormed into the lead after 17 minutes. Adriano was the guilty party, surrenduring possession in a dangerous area, from which Miki crossed for Viguera to slide home.
The visitors were given new life by the opener, and their energetic play caused more than a few problems for a suspect looking Barca defense.
But with 10 minutes to go until the break, Adriano would make amends for his earlier error. The Brazilian had already tested Sergio Herrera with a drive from range, and made no mistake at the second time of asking, linking well with Thiago before slotting under the Alaves keeper.
That goal completely floored the visitors, taking all the wind out of their sails as they settled into something of a damage-limitation exercise, with Barca moving into control.
And 11 minutes into the second half, the tie was well and truly put to bed by Villa, who flighted a perfectly-placed free kick from the edge of the area into the top corner, leaving Herrera completely beaten.
Alaves thought that it had equalized immediately after the restart when Luismi turned home a cross from close range, but the goal was chalked off on a questionable offside call, despite the winger looking level with play upon replays.
Barca wasted little time in counting their good fortune, and in an instant, added a third goal. Tello sprung past the host's backline admirably, and found himself with the time and space to tee up Villa for a straightforward finish and his second goal of the night.
From that point on, the game turned into a passing exhibition for the home side, allowing the La Masia fringe players on display to impress watching eyes, and stake their claim for a more regular place in the first team.
There was simply nothing more to come for Alaves, whose interest in the game was long ended by the time the final whistle blew, signalling the progression of the Blaugrana into the last 16.
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