Having bowed out of their home tournament four years ago with a 7-1 semi-final defeat to Germany, Brazil initially started their mission to put that humiliation behind them in stunning fashion when Philippe Coutinho struck a sublime goal to open the scoring.
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.
The five-time winners failed to extend their lead and were punished early in the second half when Steven Zuber lost his marker at a corner and equalised – a goal that might have opened the game up had Brazil been at their best.
But Tite's side remained somewhat subdued by their own high standards, with Neymar a shadow of his usual talismanic self having only recently recovered from a fractured foot, and their remaining group games with Costa Rica and Serbia now come with more pressure than would have previously been anticipated.
Switzerland can reflect on an excellent start to their campaign, having claimed a point from the most difficult of their group matches and improved their chances of reaching the knockout stages for the second consecutive tournament.
Vladimir Petkovic's side began on the front foot, Xherdan Shaqiri sending a bouncing cross towards Blerim Dzemaili that the Bologna midfielder fired over the crossbar with a shot on the turn.
Their promising start could not last and soon Switzerland were sitting back as Brazil passed the ball crisply around the pitch, almost finding a breakthrough when Paulinho dragged a shot across the face of goal and wide of the far post with 10 minutes played.
Just 10 minutes later, Switzerland were reeling from a piece of sublime, quintessentially Brazilian skill.
Marcelo's cross from the left bounced back out of the box to the feet of Coutinho, who took a touch to control it before unleashing a shot that curled spectacularly around helpless goalkeeper Yann Sommer and in off the post.
Having taken the lead, Brazil slowed the pace of the game down and frustrated Switzerland, whose only subsequent attacking foray before half-time ended disappointingly with Zuber firing a shot straight into Thiago Silva, who headed narrowly over the crossbar at the other end just before the interval.
Switzerland drew level only four minutes into the second half when a corner from Shaqiri found Zuber unmarked on the edge of the six-yard box and he had the simple task of heading the ball beyond Alisson and high into the centre of the goal.
Neymar fired into the side-netting from inside the penalty area and Fernandinho hit a speculative long-range shot wide to the left of the target as Brazil probed for a goal to restore their lead, but their attacks lacked the necessary urgency.
Coutinho had another chance to score with 20 minutes left but his neat control was followed by a wayward drive, and Gabriel Jesus saw a penalty appeal waved away when he was challenged by Manuel Akanji in the box.
Two late chances fell to Brazil substitute Roberto Firmino, but the Liverpool forward lashed the ball over before drawing a reaction save from Sommer with a close-range header, and Miranda almost made amends for his failure to mark Zuber earlier but fired wide from 18 yards as Switzerland held on for a deserved point that was secured when a Fabian Schar block prevented Coutinho from having the final say.
Key Opta stats:
- Brazil failed to win their opening match at the World Cup for the first time since 1978, when they drew 1-1 with Sweden; they had won nine in a row between 1982 and 2014.
- Switzerland have lost only one of their last 23 matches (W16 D6), a 2-0 defeat to Portugal in October 2017.
- Brazil have failed to win any of their last three World Cup matches (D1 L2), their worst winless run since June 1978, when they went four games without a win.
- Switzerland haven't lost their opening World Cup match in any of their last five tournaments (W2 D3).
- Valon Behrami became the first Swiss player to appear in four different World Cup finals – he also appeared in 2006, 2010 and 2014.
- Brazil have won only one of their last seven World Cup matches against European opposition (D2 L4), a 3-1 win over Croatia in the opening match of the 2014 World Cup.