The South American scored his first La Liga goal as the reigning Liga champions ran out comfortable winners at Camp Nou
The champions produced a scintillating display at Camp Nou to make it six wins from six games in the top flight this season, with the Brazil international opening the scoring after just five minutes.
Lionel Messi and Sergio Busquets then added goals two and three before halftime, while Alberto de la Bella grabbed a second-half consolation for Sociedad before Marc Bartra completed the scoring for the hosts.
Barca coach Gerardo Martino continued his squad rotation policy with four changes from the side that won 4-0 at Rayo Vallecano on Saturday.
Dani Alves and Busquets replaced Martin Montoya and Alex Song, while the goalscorers from the victory at the Estadio de Vallecas - Cesc Fabregas and Pedro, who grabbed a hat trick - were left out in favor of Andres Iniesta and Alexis Sanchez.
Sociedad boss Jagoba Arrasate, meanwhile, made seven alterations to the team that drew 0-0 at home with Malaga.
Only goalkeeper Claudio Bravo, Inigo Martinez, Bergara and captain Xabi Prieto retained their places, with Antoine Griezmann, and Haris Seferovic among those to come in to the starting XI.
Those wholesale changes almost paid dividends immediately as Seferovic rattled the crossbar from outside the box after only two minutes following a bright start from the visitors.
But Barca had won 17 straight home league games before Tuesday’s fixture, and normal order was resumed just three minutes later when Neymar bundled home.
Sanchez embarked on a strong run down the right, before sending in a low deflected cross that deceived Bravo and gave the 21-year-old the simplest of tasks of tapping in from three yards.
And it did not take long for Barca to double its advantage as Messi found the net with a diving header on eight minutes.
A typically free-flowing move led to Neymar standing up a perfect cross from the left that found Messi unmarked at the back post and the Argentinian made no mistake by nodding home his seventh league goal of the campaign.
Things then went from bad to worse for Arrasate when skipper Prieto was forced off with a thigh injury, and Busquets compounded his misery in the 23rd minute.
Messi somehow contrived to hit the crossbar from two yards after Alves' low delivery from the right, but Busquets was on hand to collect the loose ball 20 yards out after a poor clearance and rifle home a fine half-volley.
The champions continued to dominate thereafter and produced some mesmerizing interplay in the final third, with the only negative of the half for Martino coming when Javier Mascherano was forced off after failing to shake off a knock from an early collision with Busquets.
Barca picked up where it had left off after the interval and created four clear goalscoring opportunities within the first 15 minutes of the second half, with Messi missing twice and Neymar and Sanchez following suit soon after.
However, Sociedad got itself back into the game just after the hour through De La Bella.
Substitute Imanol Agirretxe took advantage of some lax defending from Gerard Pique before firing across the six-yard box for the fullback to convert from close range.
But Martino’s side restored their three-goal cushion on 76 minutes when substitute Bartra got in on the act by finishing from two yards after a dazzling dribble from Messi in the penalty area.
Barca then took its foot off the pedal, although Sanchez nearly added further gloss to the scoreline as he hit the post with a header in injury time.