Brazil, ranked second in the world by FIFA, were the last remaining non-European team in the tournament after Les Bleus knocked out Uruguay in Friday's first quarter-final.
But Tite's men, who badly missed the suspended Casemiro, were soundly beaten by third-ranked Belgium thanks to a pair of goals before the break at the Kazan Arena, despite the Selecao mounting a second-half fightback.
Fernandinho turned a corner into his own net to put Belgium in front, with a superb counter-attack extending their advantage.
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Romelu Lukaku's skill and strength carried the Red Devils deep into Brazil territory and Kevin De Bruyne lashed home a brilliant 20-yard rocket from the striker's pass.
Brazil could find no answer until a 76th-minute headed reply from Renato Augusto, with star man Neymar virtually anonymous other than three poor attempts to win a penalty, although referee Milorad Mazic perhaps should have pointed to the spot when Vincent Kompany dived in on Gabriel Jesus.
Neymar did finally come to life in injury time, forcing a brilliant save from Thibaut Courtois with a curling shot from outside the area, but it was not enough to sustain his team's challenge.
A pair of early corners were poorly defended by Belgium, Thiago Silva only able to turn his effort against the post before Paulinho mishit his shot when picked out in the box.
Belgium then scored from their first corner of the game in the 13th minute.
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Kompany tried to flick on Eden Hazard's left-wing delivery but the decisive touch came from his Manchester City team-mate Fernandinho, who was deputising for Casemiro and turned the ball past Alisson via his arm.
Courtois made comfortable saves from Philippe Coutinho and Willian as Brazil, playing in the quarter-finals for the seventh straight World Cup, rallied.
But Belgium, now unbeaten in 24 matches, sensationally doubled their lead by breaking from a Brazil corner in the 31st minute.
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De Bruyne advanced on the exposed Marcelo and arrowed a wonderful drive across Alisson from the edge of the penalty area after Lukaku collected the ball, turned and embarked on a 40-yard rampaging run with a perfect pass at the end to free the playmaker.
Referee Mazic waved away Neymar's penalty appeals at the end of the first half, with the official unimpressed again as the Paris Saint-Germain star went to ground after the restart.
Tite introduced Roberto Firmino for Willian at the break and the striker got the slightest of touches on a low Marcelo centre, before Mazic again refused to point to the spot when Kompany appeared to bring down Jesus.
Hazard missed a chance to wrap the tie up by firing wide from De Bruyne's pass, Courtois denying substitute Douglas Costa at the other end.
Brazil's third change yielded a goal three minutes and 14 seconds after his introduction, Augusto gliding between two static Belgium defenders to nod a flicked header past Courtois from a sublime Coutinho cross.
And Augusto could have levelled moments later, instead dragging his 20-yard shot just wide as Brazil piled the pressure on Belgium in the last 10 minutes.
Coutinho's first-time shot flew wide and yet another Neymar penalty appeal was rejected, before the world's most expensive player drew a phenomenal fingertip save from Courtois in the 94th minute.
But Belgium held on and the much-maligned Roberto Martinez will lead his side into a World Cup semi-final against France on Tuesday.
Photo Getty Images. Caption: Belgium celebrate