Xherdan Shaqiri curled a corner to the near post where Zuber climbed to power a header home amid ultimately futile protests that he had pushed marker Miranda on his way up.
Coutinho had Brazil's best chance after the break but shot wide.
The draw brings to an end Brazil's run of nine wins in opening World Cup fixtures, and both sides now trail Group E leaders Serbia, who beat Costa Rica earlier on Sunday.
Can Brazil bounce back? .
Coupe du monde - Russie / Arabie Saoudite
Supérieurs physiquement, techniquement et tactiquement, les hommes de Stanislav Cherchesov ont dominé leur sujet de bout en bout. Un succès ferait alors du bien à ses supporters qui souhaitent sans doute voir leur équipe aller plus dans cette compétition.
World Cup - Follow the Football match between Brazil and Switzerland live with Eurosport.
Many expect Brazil to claim the 2018 FIFA World Cup, and their quest to do just that begins Sunday.
Coutinho had been handed a central role behind Neymar, on his first competitive game for four months, Gabriel Jesus and Willian in a line-up filled with attacking intent from coach Tite. It was sloppy defending to give the corner away, then the goal.
Despite dictating the pace of the game, Brazil were never completely dominant and had Switzerland's rather toothless attack to thank for not taking advantage of the possession and space the underdogs were afforded. And that's Philippe Coutinho, doing Philippe Coutinho things.
Près de 90 % des Allemands veulent plus d'expulsions | Europe — Migrants
Pour réussir, un journaliste du magazine Titanic a maquillé son compte certifié en compte d'une chaîne de télévision respectée. Seehofer menace de faire cavalier seul en matière de politique migratoire.
Another alternative to watch Switzerland vs Brazil is to try out the FuboTV 7-day free trial. There are five defenders around him failing to challenge as he leaps to meet it.
The five-time champions appear to have put behind them the 7-1 defeat to Germany in the semi-finals four years ago, impressing as they eased through qualifying for Russian Federation, finishing top of the South American standings, with the most goals scored and fewest conceded.
The Brazil captain is not fully fit but Tite believes the forward is in impressive shape ahead of today's game with Switzerland.
Eight people injured after taxi hits crowds in Moscow
Russia's Interfax news agency cited a source claiming that the driver was drunk at the time of the incident. The extent of the injuries remains unclear although police say they are no life-threatening.