The full-back has been on song this season, Sport revealing that he provided his sixth and seventh assists for the Argentine alone in the recent 5-0 mauling of Celta Vigo.
Three-time defending champion Barcelona will play the first leg against its crosstown rival at Espanyol's RCDE Stadium next week.
Suarez stretched the lead in the 31st by capitalising on Pione Sisto's sloppy back pass to score for the fifth game running and Ivan Rakitic completed the rout with a header in the 87th against ex-Barca assistant coach Juan Carlos Unzue's team.
In team news, new Barca signing Philippe Coutinho won't be making his debut just yet due to an injury, but the star trio of Lionel Messi, Luis Suarez, and Andres Iniesta, who all missed the first leg, are included in the squad. Barcelona holds the slight edge heading into the second leg by virtue of its away goal in the opening leg. Messi then turned provider, lobbing a flawless pass behind Celta's back line to meet the run by Alba, who chipped Alvarez to score.
The tie was effectively over by the half-hour mark as Ernesto Valverde's charges registered a third goal on the night, Messi curling a ball behind the Celta defence and into the left inside channel for Alba to finish off. Goals from Leo Baptistao and Gerard Moreno sent Espanyol through.
Thursday's qualifiers join Real Madrid, Atletico Madrid, Leganes, Alaves and Valencia who already sealed their qualification on Tuesday and Wednesday night.
The two La Liga giants both secured their progression from the last-16, with Barca seeing off the challenge of Celta Vigo while Madrid shot down Numencia.
Sevilla also progressed with a 2-1 win at home to second-tier Cadiz for a 4-1 aggregate.