Alba has now set up seven of Messi's 22 goals this season, while Messi has set up both of Alba's strikes.
He said: "He is a player that the club has been following for a long time, we think he can help us, he is young, with projection and self-confidence for the game".
Perhaps unsurprisingly, Messi made way before the hour mark for Ousmane Dembele.
Cross city rivals Espanyol won 2-0 away at Levante in their second leg to overturn a 2-1 deficit from the first leg and they will relish the prospect of a local derby with the Camp Nou side.
I want to stay at Bayern Munich, says Ribery
However, Jupp Heynckes came out and told the media that Bayern would not be selling any players during the transfer window. The win for Bayern however highlighted a serious issue for Leverkusen as they seemed to have no plan-b.
With new signing Philippe Coutinho watching on from the stands, Lionel Messi led the destruction of the Galician side. Ivan Rakitic completed the rout late on. Barcelona's all-time scoring leader swept Alba's cross past Sergio Alvarez despite the goalkeeper getting a hand to the ball, and he followed up by firing home after another exchange of passes with Alba. "They look for each other and are happy to do so, because it is not just Alba assisting Messi". Messi tucked the ball into the bottom-right corner of the net from 14 yards out after playing a one-two with Alba to get inside the box.
Worse was to follow for Celta on 31 minutes when Pione Sisto gifted the ball to Suarez inside the box with a poor backpass and the Uruguay global smashed his shot into the top-right corner of the goal.
Barcelona extended its unbeaten run this season to 28 straight matches, dating back to its losses to Real Madrid in both legs of the Spanish Super Cup in August.
Sevilla also progressed with a 2-1 win at home to second-tier Cadiz for a 4-1 aggregate.
Thursday's qualifiers join Real Madrid, Atletico Madrid, Leganes, Alaves and Valencia who already sealed their qualification on Tuesday and Wednesday night. "We are sad, but we will get through this together".