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.
Moments later, Barca grabbed their fourth goal on the night when Luis Suarez pounced on Pione Sista's poor back pass before slotting past Alvarez.
But Coutinho, dressed in a black shirt dotted with white stars, was in the stands at the Camp Nou for the first.
Luis Suarez added the fourth before half-time after a awful back-pass by Pione Sisto left him with only the goalkeeper to beat, and Ivan Rakitic headed home from Ousmane Dembele's corner late on.
Valverde is expected to name a stronger line-up this time with Messi, Suarez and Iniesta returning to his squad after the trio played during the weekend's 3-0 victory over Levante in La Liga.
Sevilla also qualified for the quarter-finals with a 4-1 aggregate win after beating Cadiz 2-1 thanks to goals from Wissam Ben Yedder and Joaquin Correa.
Atletico and Sevilla is the matchup of teams better positioned in the Spanish league.
12 January 2018:Copa del Rey (The Spanish cup) quarter-final draw washeld on Friday, 12 January, 2018, at the headquarters of the Royal Spanish Football Federation (RFEF) Soccer City in Las Rozas, Spain. "We are all suffering from the derby loss", Correa said.
That happens to be the same scoreline by which the Blaugrana beat local rivals Espanyol when they last met back in September, with Lionel Messi contributing a hat-trick along with goals from Luis Suarez and Gerard Pique.
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