Philippe Coutinho opened the scoring in the first half with a stunning, curling strike before Steven Zuber headed home a corner in the second half to earn the Swiss a point.
Playing a World Cup match for the first time since that humiliating 7-1 defeat to Germany on home soil, and subsequent third place play-off defeat to Holland, a below-par Brazil toiled in Rostov-on-Don.
That traumatic semifinal defeat four years ago led to a period of soul searching in Brazilian football and the return of former coach Dunga.
However, the former World Cup-winning captain was sacked after a disastrous Copa America performance in 2016 that saw A Selecao knocked out at the group stage.
In came current manager Tite, previously in charge of Corinthians and Sao Paulo, to lead Brazil to seven consecutive qualifying victories, making them the first team to secure a spot in Russia after the hosts.
Yet despite being favorites for the title in Russia, Brazil's tournament debut was far from the breeze many were expecting.
Genius of Coutinho
Switzerland created the first opening of the game as Xherdan Shaqiri's cross found Blerim Dzemaili, but his acrobatic effort flew comfortably over the bar.
But it wasn't belong before Brazil got a foothold in the game and began to dominate.
Coutinho bamboozled the Swiss defenders on the edge of the area, turning this way and that, before finding Neymar down the line.
His pass across goal found its way into Paulinho's path but Yann Sommer somehow got a fingertip to the ball to turn it around the post.
Coutinho, rather than Neymar, was at the heart of everything Brazil were producing and it would be the Barcelona star who broke the deadlock in spectacular style.
Picking up the ball on the edge of the area, Coutinho curled a shot, which started well outside the far post, beyond Sommer, off the woodwork and into the far corner.
Coutinho may soon have to stamp a trademark on those types of goals, such is the regularity with which he produces them.
But after falling behind Switzerland began to play their way back into the game as the half wore on and leveled the scores soon after the restart.
Zuber escaped the attentions of Miranda and Thiago Silva in the box, heading home Shaqiri's corner from inside the six-yard box.
In truth, Brazil looked a shadow of the side that breezed their way through qualifying, a below-par Neymar exemplifying the team's struggles as a whole.
This was only the third appearance the $263 million man had made since returning from a metatarsal injury suffered playing for Paris Saint Germain in February.
Tite even admitted pre-match that Neymar wasn'