The five-time champions came to Russia desperate to make amends for their stunning 7-1 semi-final defeat to Germany in Belo Horizonte in 2014.
But three of Belgium’s so-called golden generation – Kevin De Bruyne, Romelu Lukaku and Eden Hazard – ran riot in the first half in Kazan and the Red Devils showed impressive resilience to hold on in the second period in the face of incessant pressure.
“These boys deserve to be heroes in Belgium,” said coach Roberto Martinez. “The execution of the tactics was magnificent.
“It is special and we can’t let the people of Belgium down. We can pass that down the generations – beating Brazil.”
Coming into the match, Martinez acknowledged the gulf in World Cup pedigree between his side, who have never been further than the semi-finals, and their illustrious rivals.
But after a bright start from Tite’s team, it was Belgium who looked the more dangerous, scoring through a Fernandinho own goal in the 13th minute and increasing their lead with a superb De Bruyne strike just after the half-hour.
Tite threw on Liverpool forward Roberto Firmino for Willian at half-time and the famous yellow shirts poured forward in increasing desperation, only to find an impenetrable wall at the back.
Substitute Renato Augusto gave Brazil hope with just under a quarter of an hour to go with a deft header into the bottom-right corner of the net.
Neymar had a chance to equalise late in injury time but Thibaut Courtois produced a magnificent save to tip over the goalbound curling effort.
Brazil have not lifted the World Cup since 2002 and will have to stand by and watch as a European side win it for the fourth time in a row.
“It’s a heavy, bitter feeling. This was very hard for us to swallow,” said a downbeat Tite, who refused to be drawn on his future.
France ease through
Earlier, France became the first nation to book their place in the semi-finals, making an ominous statement of intent in easing past Uruguay 2-0.
Uruguay were dealt a devastating blow before kick-off in Nizhny Novgorod when Paris Saint-Germain forward Edinson Cavani was ruled out after failing to recover from the injury he picked up in the win against Portugal.
Raphael Varane opened the scoring shortly before half-time from a set-piece, steering a header past a diving Fernando Muslera after Antoine Griezmann whipped the ball in.
But France were indebted to Hugo Lloris for pulling off a stunning save at full stretch moments before the half-time whistle to deny Martin Caceres.
Didier Deschamps's team doubled their lead in the 61st minute when Muslera made a terrible error, failing to parry a speculative shot from Griezmann and watching in horror as it looped across his goalline.
Deschamps said his side had “again raised our level” after the 4-3 win that ended Argentina’s campaign in the last 16.
“I have a good team that still has plenty of room for improvement,” he said. “You can see our lack of experience sometimes, but we have so many qualities too.
“We played well but it was not the perfect match. There are so many things that we can improve on.”
In England, World Cup fever is building as hopes rise that Gareth Southgate’s young team spearheaded by striker Harry Kene can beat Sweden in Samara on Saturday and reach the semi-finals for the first time for 28 years.
“We’ve already had our first knockout win in 12 years, our first win in a penalty shootout in a World Cup for England, the highest number of goals scored in an individual game,” Southgate said.
“We want to keep making that history,” he added. “We know that it’s not since 1990 we were in a World Cup semi-final. We’re hugely ambitious and want to do that, but we know there's nothing in our mind other than tomorrow's game.”
England or Sweden will play the winner of Saturday’s other quarter-final, in which host nation Russia will aim to keep defying the odds when they play Luka Modric’s skilful Croatia side.
Meanwhile, FIFA President Gianni Infantino told President Vladimir Putin that visitors to the World Cup had fallen “in love with Russia”, during a meeting Friday at the Kremlin.
“Everyone who has been here for a period of time now has discovered a country that we didn’t know,” Infantino said.