The Hoffenheim defender cancelled out Philippe Coutinho’s stunning first-half opener with a bullet header five minutes after the restart, with the South Americans appealing in vain for a push on defender Miranda.
In their first game at the finals since their 7-1 humiliation by Germany four years ago, Brazil created enough chances to win the game, particularly amid a late flurry, but were unable to score a second as they failed to win their opening game at the tournament for just the fifth time in 21 attempts.
Switzerland started confidently and Blerim Dzemaili even threatened to shock the five-time champions with an early flick, which flew just over the bar.
However, Tite’s men soon settled and after Swiss goalkeeper Yann Sommer had got his fingertips to Paulinho’s close-range shot following an exchange of passes between Coutinho and Neymar, they took the lead in style with 20 minutes gone.
Marcelo’s cross was cleared only as far as Coutinho, who took a touch before curling an unstoppable right foot shot beyond the keeper’s despairing dive and inside the far post.
They could have increased their lead 12 minutes before the break, when Gabriel Jesus climbed to meet Neymar’s corner, but directed his header harmlessly back in the direction from which it had come.
Switzerland responded in determined fashion, but might have conceded again in first-half stoppage time when defender Thiago Silva headed over from another Neymar delivery.
But Vladimir Petkovic’s men were back on terms within five minutes of the restart, much to the annoyance of the Brazilians.
Xherdan Shaqiri curled a corner to the near post where Zuber climbed to power a header home amid ultimately futile protests that he had pushed marker Miranda on his way up.
Brazil’s reaction was concerted as Coutinho saw two shots blocked in quick succession before Neymar’s 58th-minute shot was deflected into the side-netting.
But with the Swiss defending for dear life, the South Americans lacked composure and their efforts ecame increasingly desperate with even Coutinho falling victim when he sliced wide from a promising position with 20 minutes remaining.
Dzemaili failed to trouble keeper Alisson from distance three minutes later, but Swiss hearts were in mouths within seconds when Jesus went down in the area under Manuel Akanji’s challenge, although Mexican referee Cesar Ramos was unmoved.
Substitute Roberto Firmino added fresh impetus after replacing Jesus with 11 minutes left on the clock, but he slashed high and wide from a tight angle when a cross might have been the better option.
Neymar could have stolen the headlines with a later header from William’s cross, but directed the ball straight at a grateful Sommer, who then repelled a 90th-minute effort from Firmino.
Brazil poster boy Neymar arrived in Russia admitting he would not have paid the £200m Paris St Germain did for his services, but insisting he was ready to show the world his quality.
He looked lively in the early stages, but tired as the game wore on having missed the final three months of Paris St Germain’s season with a fractured metatarsal. His cause was not helped by some tenacious tackling which cost both Stephan Lichtsteiner and Valon Behrami bookings.
Lined up on the left side of a three behind lone striker Gabriel Jesus and asked to link up with playmaker Coutinho and target the space between full-back Lichtsteiner and central defender Fabian Schar, Neymar’s readiness to take runners inside also gave marauding full-back Marcelo the opportunity to add another supply line.
Neymar initially caused the Swiss defence major problems with his movement and ability on the ball but his influence waned as time ran down with his lack of recent action and a series of crunching challenges on him taking their toll, but he kept going manfully until the final whistle and might have won it at the death.
He did create a series of chances for others, but also had a handful of opportunities to score himself. He saw a 58th-minute shot deflected into the side-netting by Lichtsteiner, but might have done better with two minutes remaining when he headed Willian’s cross straight at keeper Yann Sommer.
That was Neymar’s final opportunity but the keeper was then relieved to see Miranda drag an injury-time volley inches wide as his side emerged with a precious point.
Alisson, Danilo, Thiago Silva, Miranda, Marcelo, Casemiro (Fernandinho 60), Paulinho (Renato Augusto 67), Willian, Coutinho, Neymar, Gabriel Jesus (Firmino 79).
Sommer, Lichtsteiner (Lang 87), Schar, Akanji, Rodriguez, Behrami (Zakaria 71), Xhaka, Shaqiri, Dzemaili, Zuber, Seferovic (Embolo 80).
Cesar Arturo Ramos Palazuelos (Mexico).