Real Madrid were held to a 1-1 home draw by newly- promoted Levante.
Barcelona further cemented their position at the top of La Liga as they defeated local rivals Espanyol 5-0.
Lionel Messi scored a hat-trick while Ousmane Dembele marked his debut with an assist.
Earlier, Madrid paid for the absence of the suspended Cristiano Ronaldo and a series of missed chances by Gareth Bale as they were held to a shock 1-1 home draw by newly- promoted Levante.
Barca, on the other hand made no such mistake. Ernesto Valverde's men have taken maximum points from their opening three La Liga games.
Messi led the way with a virtuoso performance, but his opener also needed a huge slice of luck as he was wrongly not flagged offside from Ivan Rakitic's through ball before blasting into the top corner.
Barca's second arrived thanks to a counter-attack from an Espanyol corner led by Messi and Luis Suarez before Jordi Alba's low cross was slotted home at the near post by the Argentine.
"It is a privilege to play with the best player in the world," said Suarez.
"Game-by-game he keeps showing that Messi will be around for a long time to come."
Messi put the outcome beyond any doubt by rounding off his hat-trick with another sharp finish from Alba's cut-back.
Dembele has the unenviable task of replacing the departed Neymar and Barca's 105 million-euro man had to wait until 22 minutes from time for his debut as he replaced Gerard Deulofeu to a standing ovation.
He showed why Barca have made the 20-year-old the third most expensive player ever as his pinpoint cross was swept home by Suarez to round off the scoring after Gerard Pique had headed home Barca's fourth.
However, even a fine display didn't dissuade the bad feeling towards Barca's under-fire board after a chaotic summer in the transfer market and splits between the boardroom and the dressing room, with Messi and Andres Iniesta yet to sign extensions to their contracts which expire in 2018.
Suarez's fifth goal was met with chants for president Josep Maria Bartomeu to reign.
Atletico Madrid also trail Barca by four points as without the suspended Antoine Griezmann they drew a blank in an intense 0-0 draw at Valencia.
Sevilla moved up to second, just two points behind the leaders, as goals from Paulo Henrique Ganso, Wissam Ben Yedder and Nolito secured a 3-0 win over Eibar.
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