Coming into the match on the back of consecutive defeats in the Champions League and La Liga, Barca's first losses of the season, coach Gerardo Martino deployed most of the first-choice players available to him despite their lowly opposition.
However, it was the home side who struck first at their modest Cartagonova stadium on the south coast when forward Fernando raced clear in the 16th minute and finished low past Jose Manuel Pinto.
The goal seemed to shake Barca, who were missing a slew of injured players including Lionel Messi, Xavi and Andres Iniesta, from their lethargy and they threatened several times before Cesc Fabregas sent Pedro through and he shot into the corner.
A superbly-executed Fabregas volley from Adriano's cross made it 2-1 two minutes before half time and Barca squandered several clear chances before Pedro scored his second of the night in the 76th minute from an Alexis Sanchez assist.
Teenage substitute Jean Marie Dongou added a fourth in the 90th minute when the B team forward tapped into an empty net after another Pedro effort flew back off a post.
The King's Cup format makes it hard for lower-league sides to cause an upset as the second legs are always played at the stadium of their more illustrious opponents.
Critics say the policy robs the competition of the romance of Cups in other countries, where an act of giant killing is much more likely.
In Friday's other first legs, Real Sociedad were held to a 1-1 draw at third-tier Algeciras and Sociedad's La Liga rivals Real Betis won 2-1 at Lleida, also from the third tier.
Villarreal and Elche drew 2-2 in a clash of top-flight clubs, who enter the competition at the last 32 stage, Sevilla won 1-0 at third-tier Racing Santander and Real Valladolid drew 0-0 at home to Rayo Vallecano.
Holders Atletico Madrid play their first leg at third-tier Sant Andreu and Real Madrid, last season's beaten finalists, take on Olimpic de Xativa, also from the third tier, on Saturday.
Real will be without top scorer Cristiano Ronaldo, who has recovered from a minor muscle strain but has been left out of the squad.
The return legs take place from December 17-19.
(Editing by Peter Rutherford)
