The Belgians had been put in the bracket of dark horses prior to the action getting underway in Russian Federation this summer, due to their lack of worldwide pedigree despite the wealth of Premier League talent at Roberto Martinez's disposal.
Coutinho sent another effort spinning wide as Brazil continued to create openings but failed to take any of them, with Belgium goalkeeper Thibaut Courtois tipping over a late Neymar curler to win his side the game.
Brazil chased an equaliser in the last 14 minutes of the match in the wake of substitute Renato Augusto's fine headed goal.
Coach Roberto Martinez had been criticised for not finding the right balance to get the best out of De Bruyne early in the tournament, but the Spaniard's bold tactical plan worked to perfection against Brazil.
"It was a big call to bring Marouane Fellaini back, but he stuck to his job so the system was flawless".
But after a bright start from Tite's team, it was Belgium that looked the more risky, scoring through a Fernandinho own goal in the 13th minute and increasing its lead with a superb De Bruyne strike just after the half-hour.
Widely regarded as one of the world's best goalkeepers, Courtois has won two Premier League titles with Chelsea and La Liga while on loan at Atletico Madrid, but his nine-save display against Brazil was one of his best yet on the big global stage.
We had to be fearless tactically and to do that in a World Cup, the players have to believe.
And De Bruyne feels Brazil's inability to properly adapt to Belgium's tactics ultimately cost them. You are the top dog for a team and an organization that has done really well for many, many years.
'My all-round game is always my strong point, I try to make other players better, I want to score as much as possible and also give as many assists as possible, and I am very busy with the team, so I can be important too'.
"Against them, there's a psychological barrier - the yellow tops, the five world titles and everything that goes with that", Martinez told reporters of facing Brazil.
Belgium and France will meet in St. Petersburg on Tuesday.
If Belgium's first goal in the 13th minute had an element of luck, with the ball going into the net off Fernandinho's shoulder from a corner, the second in the 31st minute was a percfect example of counter-attacking football.
Fernandinho of Brazil is challenged by Nacer Chadli of Belgium during the World Cup quarterfinal.
England sink Sweden to clinch World Cup semi-final berth
England cruised by Sweden to book their place in the last four of the World Cup, reaching their first semi-final since Italia 90. The trio have not clicked, and it has been a combination of set pieces and captain Harry Kane that have made the difference.