Brazil hasn't lost its opening match in the World Cup since falling 3-1 to Spain in 1934.
The South Americans continued to dictate terms after that and took the lead in the 20 minute when Philippe Coutinho curled a spectacular 22-yard effort into the top corner, 1-0. It was Coutinho's 11th goal in 37 matches with Brazil.
Switzerland's Steven Zuber heads the equaliser in a 1-1 draw with World Cup favourites Brazil. Brazil has won its group in every World Cup since 1982 and most recently failed to get out of the first round in 1966.
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Star forward Neymar was back in action after suffering a foot injury earlier this year, and scored twice with flair in the last two matches.
However, Brazil failed to build on their lead as Thiago Silva and Jesus headed off target from unsafe corners and were made to pay early in the second half.
Switzerland goalkeeper Yann Sommer can't stop a shot from Brazil's Philippe Coutinho.
Brazil pushed hard for the victor - with Neymar heading right at Yann Sommer in the Switzerland goal in the 87th minute and Roberto Firmino doing the same soon after - but had to settle for a draw and one point that leaves them in a tie for second place in their group.