But Roberto Firmino, Augusto and Coutinho could not convert gilt-edged opportunities to level the scores. Lukaku quickly darted into the heart of Brazil's midfield and easily fed De Bruyne who launched a long-range laser past a diving Alisson for the 2-0 lead at the 31st minute.
Roberto Martínez described himself as "the proudest man in the world" after his Belgium side demonstrated tactical nous and then tremendous desire to beat Brazil and reach the semi-final of the World Cup for the first time in 32 years.
That freed De Bruyne to play in a more advanced role and the City midfielder revelled in the space Brazil continually gave him.
This was no repeat of Belo Horizonte four years ago, when Brazil were thrashed 7-1 by Germany in the semi-finals on home soil, and Tite's side kept their shape and composure despite trailing by two goals.
But it was too late for Brazil to muster an equalizer as Courtois thwarted several efforts to force the game into extra time.
The victor will play France or Uruguay in the semifinals in St. Petersburg on Tuesday.
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"It was a very impressive game between two teams with fantastic technical qualities", he said.
Brazil's World Cup came to a premature end on Friday, when the five-time victor was eliminated from the competition following a 2-1 loss to a talented Belgium side at Kazan Arena. If you aren't scheduling your entire life around World Cup, you'll be happy to know fuboTV provides access to all of the games for up to 72 hours after the original airing, allowing you to watch the games on your own schedule.
And they're finally beginning to play like a well-gelled unit.
"We are leaving the World Cup with sadness", said Brazil skipper Miranda.
Both teams have looked awesome to this point, so Courtois will try to lead Belgium's golden generation to another win and an appearance in the final. But the defense was breached after 13 minutes in Tatarstan. But Brazil looked impressive against Mexico, and with Neymar getting fitter and more effective with every outing, the Belgians should be concerned.
The outcome sparked jubilation in Belgium - and much soul-searching in Brazil.
With Casemiro, things might have been different, but manager Tite should have known better and gone with Augusto from the start.