Valencia also cruised through by thumping third-tier Cadiz 4-0 after drawing 0-0 at the south coast club in the away leg.
Braces from Thiago Alcantara, Cristian Tello and Isaac Cuenca and one goal each from Andres Iniesta, Xavi and Pedro thrilled the 60,000 fans at Barca's Nou Camp, although the festival was soured slightly by a minor injury to Iniesta.
The Spain playmaker, who had to be replaced after half an hour, damaged a thigh muscle but should be fit for Barca's next match, a La Liga game at city rivals Espanyol on January 7, the club said.
In the earlier kick-off at the Mestalla, Cadiz's bid to upset Valencia was set back in the fifth minute when Victor Ruiz nodded the home side in front.
Playmaker Jonas and striker Roberto Soldado made it 3-0 by half-time and Ever Banega added a fourth with just over 20 minutes remaining.
The draw for the next round is on Friday.
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