Belgium were gifted the lead through an unfortunate own goal from Brazil star Fernandinho after 13 minutes.
The Red Devils doubled their lead on the half-hour mark via an exquisite 20-yard finish from Kevin De Bruyne.
Renato Augusto pulled one back for Brazil with a good header just three minutes after coming off the bench.
Brazil denied a penalty despite Vincent Kompany appearing to bring Gabriel Jesus down in the penalty box.
Belgium will face France in the World Cup semi-final on Tuesday 10 July, 7:00pm.
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