Switzerland have lost only one out of 12 competitive matches since Euro 2016 - a World Cup qualifier away to Portugal.
Philippe Coutinho gave Brazil the lead in the 20th minute with a volley that bounced in off the right post.
But Switzerland stood up to the Selecao with the equalizer in the 50th minute on a Steven Zuber header. Mexican referee Cesar Ramos dismissed complaints that Zuber had shoved defender Miranda before getting to the corner from Xherdan Shaqiri. "In the second half, I told them to remain calm, focused, believe in ourselves and try and push higher up on the pitch and create possibilities and opportunities to score, and that's what we did".
Gabriel Jesus also appealed for a penalty when he clashed with Manuel Akanji in the box, but Marcelo did not want to make excuses for Brazil's inability to turn a dominant display into three points.
Switzerland played physical, fouled plenty to try and slow down Brazil's rhythm, and it earned a surprising result that puts them in a great spot moving forward.
Neymar gets up after falling to the ground during Brazil's draw with Switzerland.
But Brazil ignominiously bowed out of the World Cup four years ago - losing to Germany 7-1 in the semifinals and falling 3-0 to the Netherlands in the third-place game.