The result was overshadowed by a medical emergency in the stands, though, which led to the referee halting the match with less than 10 minutes remaining.
Cadiz goalkeeper Jeremias Ledesma was seen throwing a medical kit into the stands due to the health emergency, which led to a delay in the contest, but after the best part of an hour, the players eventually returned to the field to finish the game.
"[The fan] regained the pulse, and has been brought into an ambulance. [The fan] was revived, fell ill again, but was eventually stabilised. It looks as the match will be finished," Cadiz president Manuel Vizcaino has been quoted as telling Tiempo de Juego.
Barcelona had to wait until the 55th minute to take the lead, with Frenkie de Jong, who was strongly linked with an exit over the summer, finishing from close range.
The away side's second arrived in the 65th minute when Robert Lewandowski converted after Ledesma had saved from the lively De Jong.
Barcelona were two goals ahead when the match was temporarily postponed, but they scored twice more in the latter stages, with Ansu Fati and Ousmane Dembele rounding off a strong win for Xavi's side.
Fati was on hand to convert after strong work from Lewandowski, while Dembele continued his strong run of form by netting after a mazy run at the Cadiz defence.
The match saw Hector Bellerin and Marcos Alonso both make their debuts, with the former starting at right-back, while the latter came off the bench in the 78th minute.
Barcelona have now picked up 13 points from their five league matches this season, which has seen them move a point above Real Madrid, who are in action on Sunday against Mallorca.