They had to score twice to get through after conceding two away goals in the 2-1 first leg defeat and just quarter an hour they had their first.
For Celta, keep an eye on their No.10 Iago Aspas.
With the goal, he became the top scoring midfielder in the La Liga. They ended 2017 in the best way imaginable with a 3-0 win over Real Madrid, and beat Levante by the same scoreline in their most recent encounter.
Sevilla defeated fellow Andalusian side Cadiz 2-1 at home for a 4-1 aggregate win, while Espanyol overturned a 2-1 deficit from the first leg by beating Levante 2-0 away to join Barca in Friday's quarterfinal draw.
Manager Juan Carlos Unzue will be hoping for another big showing from his players at the Camp Nou, but whether they can produce a third high-intensity performance in a week remains to be seen, and it will be tougher for Celta on Thursday as Barca boss Ernesto Valverde is likely to field a stronger line up than he did in the first leg.
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"We can't think that the result is in our favour because then there is the risk that we will make a mistake", he continued. "Our intention is to try to dominate the match".
Valverde's chosen squad for the game includes Jasper Cillessen, Marc-Andre ter Stegen, Nelson Semedo, Gerard Pique, Javier Mascherano, Thomas Vermaelen, Jordi Alba, Lucas Digne, Sergi Roberto, Sergio Busquets, Ivan Rakitic, Iniesta, Paulinho, Andre Gomes, Carles Alena, Messi, Suarez, Ousmane Dembele and Jose Arnaiz.
Celta have no injury concerns ahead of the game.