Gavi and Jules Koundé scored a goal each in the first half-hour and Raphinha, Ferran Torres and Lamine Yamal added to the lead in the second half to give the Catalan club the win and a spot in the quarterfinals.
Wednesday's was the fourth straight victory in 2025 for Barcelona, and came after they defeated Madrid 5-2 in Saudi Arabia on Sunday to win the Spanish Super Cup.
"We wanted to keep the momentum from the Super Cup here at home in front of our fans," Barcelona defender Pau Cubarsí said.
"We continue like this and keep the foot on the throttle. The (Christmas) break did well for us, we were able to refresh."
In other cup ties, Atletico Madrid, playing without many regular starters, easily accounted for second-division club Elche 4-0 to extend their record winning streak to 15 matches.
The club had never won more than 13 games in a row across all competitions before.
Alexander Sorloth scored from close range in the eighth minute and converted a 29th-minute penalty kick.
Rodrigo Riquelme scored the third from long range in the 61st, and Julián Álvarez closed the scoring in the 75th.
Meanwhile, Getafe scored two minutes into their match with fourth-division club Pontevedra for a 1-0 win.
And an 86th-minute goal by Diego García gave Leganes a 3-2 win at second-division club Almeria.
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