A fearless Belgium showcased their attacking brilliance then survived a spirited Brazilian fightback to claim a 2-1 win over the tournament favourites at Kazan Arena and reach the last four for the first time in 32 years.
Belgium beat them 2-1 on the night to secure a first World Cup semi-final since Mexico 1986.
The teams meet at the World Cup for the first time since 2002 when Brazil won 2-0 in the last-16, before going on to lift the trophy.
A Fernandinho own goal and fierce strike from Kevin De Bruyne put Roberto Martinez's side in early control of a compelling encounter. In the past 25 matches under head coach Tite, Brazil have conceded only six goals and kept 19 clean sheets.
It was a attractive counter-attack finished in sublime fashion by De Bruyne, shortly after the half hour mark, leaving Brazil facing a challenge that no side had overcome in World Cup history - winning a game after trailing by two at half-time, excluding penalties.
It takes some luck to advance from any doe-or-die game, especially at a World Cup. After Belgium cleared a corner, Lukaku turned into space and burst down the middle.
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.
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.
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Ther bad news for Brazil is that they have been knocked out of the World Cup by European sides in the last three editions.
For Brazil, hopes lie on the feet of world class forward Neymar, but Paulinho and Philippe Coutinho have combined for some brilliant offense that has stretched defenses and only strengthened the Seleção's possession-oriented game. Brazil was slow out of the gate in its 2-0 victory over Mexico Monday, but so was Belgium. "Just treasure it and pass it down in the generations". Even referees could be influenced by this controversy and punish Neymar unfairly, but he must try to relax and I believe manager Tite would try to calm him down, telling him to just play his game as he always does.
"This was the biggest test for us, " De Bruyne said.
"The games aren't for coaches, they're for players, you have to help the players be themselves on the pitch".
"It was a very impressive game between two teams with fantastic technical qualities", he said. The playacting and diving, though, have made him a figure of mockery, especially in Europe.
And a lot of that was down to a wonderful save from Thibaut Courtois in injury-time from a superbly hit shot from Neymar.
"Many aspects made me proud".
VAR came into play soon after the Neymar penalty shout when Kompany tripped up Jesus near the Belgium goalline, but after review the video assistant did not award a spot kick to Brazil.
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