Hazard, for his part, captained Belgium as they overturned a 2-0 deficit against Japan, assisting the equalising goal.
Neymar now has two goals to his name for Brazil during the tournament and will look to add to his tally when they take on Belgium in the quarter-finals this evening.
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.
"Only a few times in your lifetime [can you come to a World Cup], you might go to two or three in a lifetime if you're lucky".
"I don't care where I play". Defence is one of the strong points of the the current Brazil side, who have conceded just once in their four matches. "And that way, by defending, we're already in a position to win the ball back if we lose it".
Not when Courtois was proving to be an impenetrable barrier in the Belgium goal, denying Marcelo's strike before the lead was extended.
Against Brazil, again it was Lukaku's link-up play that proved decisive as he powered past Fernandinho and Paulinho on a rapid counter-attack before feeding De Bruyne to smash home from the edge of the area.
"I thought it was a great match and we had a lot of it, with plenty of possession and a lot of opportunities", said a shellshocked Tite after the match.
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.
Though Belgium and Brazil are evenly matched in terms of quality, coach Roberto Martinez said there's a simple difference between the two teams.
The Manchester City player will remain with the squad while undergoing treatment.
Lukaku was, of course, once on Chelsea's books - as was his Belgium teammate De Bruyne.
Everything changed in the 76th minute, when Philippe Coutinho curled the ideal ball toward te penalty spot where Renato Augusto was waiting and anticipating.
The loss marks the third time in four World Cups that Brazil has been eliminated in the quarterfinals.