The five-time champions, so often lauded for their flair, failed to sparkle after Philippe Coutinho’s superbly curled opener on 20 minutes.
Philippe Coutinho lit up the Rostov Arena with one of the best goals of the World Cup so far but it was not enough to see the tournament favourites start with three points.
The Barcelona ace curled in a superb opener from long range after 20 minutes, but Switzerland hit back with a Ronald Zuber header that left Brazil complaining to referee Cesar Arturo Ramos.
Tite’s side – with Gabriel Jesus and Willian alongside Neymar in a front three – could offer only fleeting moments of fluid play and Steven Zuber’s header from a corner earned the Swiss a deserved point.
Brazil may point to a push by Zuber to free him from his marker but the fact Coutinho’s strike remained their only effort on target until 77 minutes points to their struggles in the final third.
The draw brings to an end a run of nine wins in their opening World Cup fixture and both sides now trail Serbia, who beat Costa Rica earlier in Group E.