Pre-tournament favourites Brazil failed to win their opening game of a World Cup for the first time since 1978 as Switzerland earned a valuable draw in Rostov-on-Don.
The five-time champions, so often lauded for their flair, failed to sparkle after Philippe Coutinho's superbly curled opener on 20 minutes.
Tite's side - with Gabriel Jesus and Willian alongside Neymar in a front three - could offer only fleeting moments of fluid play and Steven Zuber's header from a corner earned the Swiss a deserved point.
Brazil may point to a push by Zuber to free him from his marker but the fact Coutinho's strike remained their only effort on target until 77 minutes points to their struggles in the final third.
The draw brings to an end Brazil's run of nine wins in opening World Cup fixtures, and both sides now trail Group E leaders Serbia, who beat Costa Rica earlier on Sunday.
Late intensity not enough for Brazil
Neymar's header - straight into the hands of Yann Sommer with minutes to go - summed up a Brazil performance lacking in cutting edge. Indeed, only in the dying stages did they look desperate to win, with substitute Roberto Firmino's header forcing a save and defender Miranda blasting wide.
Buoyed by a run of form showing just one loss in 21 matches and the return from injury of the talismanic Neymar, expectation is high that Brazil can banish painful memories of a 7-1 semi-final defeat to Germany on home soil four years ago.
Only Marcelo started in Russia from their line-up on that humiliating night, and one defeat in 18 qualifying matches does indeed point to a team somewhat healed.
Coutinho - chosen as the creative force in a three-man midfield also comprising Paulinho and Casemiro - stepped up to increase Brazilian positivity with a sublime effort from 20 yards which went in off the post, such was its accuracy.
It should have served as a catalyst, but with Neymar constantly harassed by the excellent Valon Behrami, clear-cut chances were hard to come by.
Coutinho chested down but fired wide after Zuber had levelled and only a clever Fabian Schar flick in his own goalmouth denied a late winner. But the fact Switzerland had 45 per cent of the ball underlines how they remained competitive throughout.
In a World Cup where sides have shown promise without being scintillating, Tite and the passionate Brazilian public are unlikely to be too worried at this stage, and Switzerland are after all the world's sixth-best side on ranking.
But those hoping to see the free-flowing football Brazil are revered for will hope they find a better rhythm against Costa Rica on Friday, and that Neymar and those around him apply from the outset the late intensity they showed here.
Job done for precise Swiss
Switzerland's haul of nine wins from 10 matches in qualifying and victory over Northern Ireland in the play-offs points to a well-drilled and highly capable side.
They paid close attention to Neymar and fouled him 10 times in all, the highest figure for a single player at a World Cup since 1998.
Former West Ham midfielder Behrami lasted 70 minutes and repeatedly broke up play, while 22-year-old defender Manuel Akanji won possession nine times and saw more of the ball than anyone on his side, impressing in just his eighth international.
This was a Swiss performance expertly mapped out but it was always going to be key to take the chances that came their way.
Zuber, making just his 14th appearance, delivered on that front, powering home from four yards after fending off the attentions of his marker. The ease with which he found the net perhaps raises questions about Brazilian defensive frailty going forward.
But Switzerland, and manager Vladimir Petkovic in particular, will care little.
Stoke's Xherdan Shaqiri carried enough threat to pose problems for others in the tournament, and while this was a display more intent on thwarting Brazil rather than pushing forward, they will be thrilled to have a point on the board going into Friday's game with Serbia.
'Too much showboating' - what they said
Brazilian football journalist Tim Vickery: "There's a lot of controversy going on in Brazil over the [Swiss] goal as lots of people feel there was a push on Miranda. But Brazil have to look at themselves tonight.
"Neymar, who is capable of brilliant things, was showboating too often and this tournament will be a test of his temperament."
Brazil coach Tite: "We had too many balls off target, if we had been a bit more focused we could have made the goalkeeper work a bit more. My expectation of course was to get a victory and of course I'm not happy with the result.
"It (Switzerland's goal) has nothing to do with positioning, it was a foul."
Switzerland coach Vladimir Petkovic: "I hope they will start taking notice of us and taking us seriously. Sometimes if there is a lack of recognition that is a pity because we have played very well. We showed and demonstrated that this team always believes in itself and can achieve results."
Sturdy Swiss maintain impressive run - the stats
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