The Barcelona full-back ensured their first match since their Confederations Cup win ended in defeat for Luiz Felipe Scolari's men
Switzerland brought an end to Brazil’s 11-match unbeaten run as Dani Alves headed into his own net to hand the hosts a shock 1-0 win.
The Barcelona defender failed to control a swinging cross from Xherdan Shaqiri and put the ball through his own goal with 47 minutes gone.
The victory for Switzerland marks their first since 1989 against the five-time world champions.
Hitzeld fielded a strong side for the match, including veteran Philippe Senderos as well as promising Bayern Munich youngster Shaqiri.
His Brazil counterpart Luiz Felipe Scolari opted to stick with nine of the XI who had won the Confederations Cup final against Spain, with Julio Cesar and David Luiz absent.
The visitors started strongly, piling on the pressure – and it looked like they would be rewarded in the 11th minute when Fred shook off his man to feed Hulk, but quick reactions from Diego Benaglio saw the 27-year-old’s shot kept out.
The home side continued to struggle to retain possession, and the Wolfsburg goalkeeper was called into action again a few minutes later. Hulk was once more involved as he charged at goal, but his shot fell well for Benaglio, who saved with his feet.
Switzerland did pose some threat on the break, but their finishing was wayward.
Tempers began to fray shortly before half-time, when Stephan Lichtsteiner was chopped down by Neymar, with the Barcelona striker earning a yellow card as referee Deniz Aytekin struggled to separate the players.
Brazil should have opened the scoring when Paulinho’s header came back off the crossbar, before Shaqiri tested Brazil goalkeeper Jefferson with a long-range effort at the other end.
At the break, the hosts withdrew Valentin Stocker for Tranquillo Barnetta, while 21-year-old Fabian Schaer made his international bow at the expense of Senderos.
The changes reaped rewards within a few minutes, as Switzerland’s pressure ended with a cross from Shaqiri and Alves inadvertently headed past his own keeper.
Brazil's embarrassment was almost increased soon after when Jefferson failed to control a ball leading to a melee in the box, with Haris Seferovic just beaten to it by the Brazilian.
Scolari opted to make three changes to force the game, with the most notable seeing 31-year-old Paris Saint-Germain defender Maxwell make his international debut while Fred – who has scored five in five for Brazil – left the field to be replaced by Jo.
That did not seem to help the visitors, who still found themselves battling against the impressive Swiss attack – which was typified through Shaqiri, who once again fired over the crossbar.
Brazil attempted to fight back in the latter stages, going close through Jo, but debutant defender Michael Lang intercepted.
The loss marked the first for Brazil since February, while Switzerland gained a confidence-boosting win ahead of the resumption of their World Cup qualifying campaign.