A Fernandinho own goal and a brilliant Kevin De Bruyne strike earned Belgium a date with neighbours France in St Petersburg on Tuesday, their second trip to the last four at a World Cup after 1986.
Brazil will depart at the last eight stage for the third time in the last four World Cups despite the best efforts of talismanic forward Neymar, who followed Argentina's Lionel Messi and Portugal's Cristiano Ronaldo out of the tournament.
They go out with their heads held high, though, after leaving everything on the pitch as they chased an equaliser in the last 14 minutes of the match in the wake of substitute Renato Augusto's fine headed goal.
Roared on by the vast majority of the crowd at the Kazan Arena, the Brazilians poured forward to try and keep their campaign alive but Roberto Firmino, Augusto and Coutinho could not convert gilt-edged opportunities to level the scores.
It is Belgium's latest "golden generation", therefore, who will take their place in a World Cup semi-final lineup guaranteed to be all-European and for the first time not featuring one of Brazil, Argentina or Germany.
"I think I'm the proudest man on earth at the moment," said Belgium's Spanish coach Roberto Martinez.
"For me, Brazil are the best team in the tournament and without a doubt the biggest threat from open play. We had to defend well for 90 minutes. But I felt our performance merited the opportunity to go through."
DE BRUYNE STUNNER
If Belgium's first goal in the 13th minute had an element of luck, with the ball going into the net off Fernandinho's shoulder from a corner, the second in the 31st minute was a percfect example of counter-attacking football.
Man of the Match De Bruyne, playing in a more advanced role than he had in Belgium's previous four matches, was at the heart of his team's best work, managing the transition from rearguard defence to attack with vision, pace and accuracy.
There was to be no repeat of four years ago when Brazil were thrashed 7-1 by Germany in the semi-finals on home soil, however, and they kept their composure despite conceding two goals for the first time in 26 matches under Tite.
Tite, who said it was not an appropriate time to discuss his future as Brazil coach, felt the difference in the match had been Belgium's finishing.
"It was a very impressive game between two teams with fantastic technical qualities," he said.
"For all the pain I feel right now, if you like football, you have to watch this game. It's going to give you pleasure.
"If you're a neutral, you can sit back and say, 'What a match!' Anyone who appreciates football can see that this was a beautiful game."