Brazil went all out in pursuit of a victor and came agonisingly close to finding it as Coutinho and Miranda lashed wide from inside the area while Neymar and substitute Roberto Firmino were denied by Swiss goalkeeper Yann Sommer.
The only time Switzerland and Brazil previously met in the World Cup came in 1950, when Swiss Jacky Fatton scored in the 88th minute for a 2-2 draw.
Switzerland had the first shot on goal in the third minute when a clever right-side ball from Xherdan Shaqiri found Blerim Dzemaili in space inside the box, but he fired just over from ten-yards out. The only Swiss man in there, Steven Zuber, has a free header.
But Tite's side failed to build further momentum, as Neymar was frequently stopped in his tracks by tactical fouls - a total of 10, the most since England's Alan Shearer was fouled 11 times against Tunisia on June 15, 1998 - from Vladimir Petkovic's side. "I guess that will be normal [to be fouled regularly], we have to pay attention to it, but that's something normal in football".
"It's not up to me, there are three professionals working there", said Neymar, referring to the officials. They have to do their job. "We got a draw, but this is only the beginning for us. We will continue to play with this consistency". "Now we need to think about the next match".
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Everybody is going to work extremely hard to get out of this and it will be an absolutely top effort in Cape Town. You're always going to have a hard run. "It is about sticking together, understanding what you can improve".
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The 26-year-old was playing his first competitive game since picking up a metatarsal injury while representing Paris Saint-Germain in Ligue 1.
And last but not the least, he revealed that he drove all the way back to Switzerland from Germany to watch the World Cup match at home and praised Switzerland's efforts in the game, before wishing the Brazilian team luck as well.
So, this is how Group E is looking after today's fixtures. Entering the match with a unique new hairstyle, the PSG forward struggled to make an impact and was heavily slated by the Brazilian media.
"I was hit and it was aching, but [it's] nothing to worry. after your body is cold, it aches a little more but that's OK", he said.