Neymar, who appeared in great form when scoring once and setting up another in a 2-0 last 16 win over Mexico, failed to spark on the night despite testing Belgium 'keeper Thibaut Courtois at the death.
It's the latest surprise in a tournament full of upsets, which has included Spain's shocking loss to Russian Federation in the knockout rounds and, even more surprisingly, Germany crashing out of the group stage.
There's not much to choose between the World Cup favourites and the tournament's top scorers - but one of them will soon be going home.
Of the remaining teams, France, another popular pick to win it all at the outset, is likely the new favorite. "Wherever I play, I have to contribute", De Bruyne said. Or maybe this is year that England finally, finally, wins another major worldwide tournament.
Either England or Sweden will face either Russian Federation or Croatia in the other semifinal match on Wednesday in Moscow - a day after Belgium plays France in St. Petersburg.
Unbeaten in their last 15 games, Brazil's bid for a second consecutive place in the semifinals looked in safe hands.
Romelu Lukaku took the ball with his back to goal, turned into space and stormed past Fernandinho up the pitch before releasing De Bruyne on his right for the playmaker to rifle the ball into the net from the edge of the box.
Coutinho - who had been Brazil's best attacking player in this World Cup so far - had a golden chance to equalize the game in the 84th minute.
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Belgium will face France in the semifinals on Tuesday in St. Petersburg. The next day in Moscow, it will be either England or Sweden against either Russian Federation or Croatia.
Fernandinho's World Cup woes continued, Hazard's corner coming off the midfielder's arm to glide past Alisson and into the net as he rose to block.
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. The Belgian would like nothing better than a repeat of the 4-0 scoreline that PSG inflicted on Barcelona and Neymar in the UEFA Champions League last season, which came before the Brazilian decamped to the French capital to link up with fellow countrymen Marquinhos and Thiago Silva.
Hazard dictated the tempo of the game, pressing the accelerator for counter-attacks that ripped open Brazil's defence but also, especially in the second half, slowing down play and maintaining possession.
"And now who is going home?" he wrote in an Instagram story.
De Bruyne then completed a counterattack launched by Lukaku to double the lead in the 31st minute.