Messi netted twice in two minutes inside the opening quarter of an hour, steering home from two Alba crosses, before he returned the favour with a sumptuous pass that allowed the full-back to score his second goal of the season. The Galicians held the Catalans to a 2-2 draw in early December before the 1-1 stalemate in the first leg of this tie.
Argentinean Messi scored in the 13th and 15th minutes following passes from left-back Jordi Alba.
Barca's onslaught continued with goal number four on 31 minutes, as Luis Suarez pounced on a sloppy backpass from Pione Sisto to hammer a first-time finish beyond the reach of Alvarez. Messi then turned provider, lobbing a ideal pass behind Celta's back line to meet the run by Alba, who chipped Alvarez to score.
Suarez soon got in on the act as he capitalised on a terrible mistake by Pione Sisto, who attempted to pass the ball back to his goalkeeper.
Celta improved a little after half-time but the damage had been done long before Rakitic's header completed the rout, meaning Barca will join Deportivo Alaves, Leganes, Real Madrid, Espanyol, Sevilla, Atletico Madrid and Valencia in the last eight.
Dark Souls Remastered: No HDR on PS4 Pro
The only option for American gamers who want to get their hands on the Dark Souls Trilogy, then, will be to import it. Dark Souls: Remastered is now pending a final rating with the ESRB and will carry a MSRP of $39.99 on consoles.
Goals by forwards Leo Baptistao and Gerard Moreno helped Espanyol to a 2-0 victory at Levante, sending the Barcelona-based team through 3-2 on aggregate.
Sevilla beat Cadiz 2-1 with goals from Wissam Ben Yedder and Joaquin Correa to advance 4-1 on aggregate.
"I would say I'd prefer not to draw Real Madrid", Valverde admitted in his news conference after the game.