But Roberto Firmino, Augusto and Coutinho could not convert gilt-edged opportunities to level the scores.
Fernandinho put into his own net after just 13 minutes before De Bruyne struck home into the bottom corner from the edge of the box past Alisson on 31 minutes. Belgium has scored 12 goals in the tournament, with Romelu Lukaku sitting in second place in tournament scoring with four of those goals in three matches.
De Bruyne easily ranks among the most talented players in the entire tournament―let alone Belgium's squad―but the midfielder hadn't been at his best for the Red Devils in a long time, dating all the way back to the loss against Wales at Euro 2016.
Humiliated 7-1 by Germany in the semifinals fours year ago on home soil with Neymar out injured, Brazil didn't even get that far this time.
Neymar had a late chance to equalise but Thibaut Courtois tipped over as Belgium clung on.
But they will now head into a semi-final against France with huge confidence after taking the scalp of Brazil.
"Now we need more energy for the next game, " Martinez said, "so let's make sure that we're all together and we're all driving each other to be as good as we can.in the semifinal".
Setback as Thai cave rescuers race to get 12 boys, coach out
They are being looked after by seven members of the Thai navy SEALs, including medics, who were staying with them in the cave. They have also been shown how to use diving equipment in case they are required to dive in order to get out of the cave.
Belgium led World Cup favourites Brazil 2-0 at half-time in their quarter-final on Friday as the tournament in Russian Federation braced for a major shock.
"The greatest challenge of a World Cup is having mental fortitude".
Brazil were almost back on level terms twice soon after, but Augusto fired his shot from just outside the area wide of goal before Coutinho skied a shot from Neymar's laid-off pass well over the bar.
Roberto Martinez's side will meet fellow European nation France after beating tournament favourites Brazil 2-1 in Kazan.
The introduction of Douglas Costa for the misfiring Gabriel Jesus in the 58th minute spurred Brazil on to stage a comeback with the Juventus winger putting up a fine individual display which appeared to inspire his teammates to push for a goal.
And they're finally beginning to play like a well-gelled unit. Brazil to go through 3-1 and move closer to that sixth world title.
Announcing that Marcelo will return to the left-back position against Belgium, Tite said that Brazil will bank on team work and the individual skills of their formidable forward line, which includes Paris Saint-Germain super star Neymar.