Fresh from their success in the Spanish Super Cup at the weekend, Xavi's side proved to be too strong for the hosts, who conceded either side of the half-time interval to allow the Catalan giants to take control.
Barcelona are the most successful side in the history of the Copa del Rey, winning the trophy on 31 occasions, and they have now advanced to the final eight, with Robert Lewandowski grabbing a brace in the five-goal success.
Ceuta had a golden chance to take the lead in the 30th minute when Rodri found himself free inside the Barcelona box, but the forward headed just wide of the post.
The home side were excellent for long stages of the first half, but they conceded in the 41st minute, with Raphinha collecting a pass from Franck Kessie before picking out the back of the net with a brilliant effort.
Barcelona then delivered a killer blow to Ceuta in the early stages of the second period, with Lewandowski finding the bottom corner after Kessie had delivered a low cross into his teammate.
Kessie came close to a third in the 52nd minute, but the midfielder's effort flew just wide, before Ferran Torres tested the gloves of Ceuta goalkeeper Tomas Mejias two minutes later.
Xavi's side did manage to make it 3-0 in the 70th minute, though, when Ansu Fati broke into the home team's penalty box before finding the far corner of the net.
Kessie finally got in on the act in the 77th minute, heading a Raphinha cross into the back of the net, before Lewandowski netted his second in the final minute, with the striker finding the far corner off an assist from Eric Garcia.
Next up for Barcelona is a La Liga clash with Getafe on Sunday evening, while Ceuta will resume their league campaign at home to Cultural Leonesa on Sunday morning.