The Red Devils were dominant throughout the match played at Stadium de Toulouse after Toby Alderweireld headed them into the lead in the 10th minute.
With time running out, Marc Wilmots side wasted several chances to put the game to rest, as De Bruyne failed to make use of a free kick which was deflected and another two shots which ended up over Kiraly’s crossbar.
It was not until the 78th minute that the advantage was doubled for Belgium. Michy Batshuayi came off the bench to punish Hungary when he ran in unmarked to fire a close-range shot past Kiraly.
Eden Hazard made it 3-0 for the Red Devils with a strike from the edge of the area two minutes later before Carrasco added their fourth on the stroke of time as he powered down the middle on the counter to beat Kiraly.
The resounding victory helped Belgium set up a July 2 quarterfinal clash with Wales who edged out Northern Ireland 1-0 earlier on June 25.
In other Round 1/8 matches, Poland beat Switzerland 5-4 in penalties following a 1-1 draw; Portugal saw off Croatia with Quaresma’s solitary goal in extra time; France knocked out Ireland 2-1; and Germany thrashed Slovakia 3-0.
