Belgium struck early and held off a late Brazil fightback to send the five-times champions tumbling out of the World Cup with a 2-1 victory in an end-to-end thriller on Friday that earned them a semi-final against France.
A Fernandinho own goal and a brilliant Kevin De Bruyne strike gave Belgium a spot in the last four for the second time after 1986 and sent Brazil home at the quarter-final stage for the third time in the last four World Cups.
Brazil dominated possession and carved out chance after chance but, despite the best efforts of Neymar, were unable to find the net until substitute Renato Augusto headed home Philippe Coutinho's cross 14 minutes from time.
Roared on by the vast majority of the crowd at the Kazan Arena, the Brazilians poured forward to try and save the game but Roberto Firmino, Augusto and Coutinho spurned gilt-edged opportunities to level the scores.
Neymar continued to run at the Belgium defence until the end but had a second penalty appeal waved away by Serbian referee Milorad Mazic and a final shot tipped over the bar by Belgium goalkeeper Thibaut Courtois as the last few seconds ticked away.
"They did it... they were incredible, incredible hearts out there," said Belgium's Spanish coach Roberto Martinez.
"I didn't think for one minute they were going to give up... (our) execution was magnificent. When you say we are going to play in a certain way, they changed their tactical disposition and tactics... it (our gameplan) was executed to perfection."