Eden Hazard, substituted ten minutes from full-time, left the field to a standing ovation from both sets of fans moments after scoring Belgium’s third goal, having given a masterclass that booked his side a quarter-final clash with Wales in Lille on Friday.
The highest-valued squad in the tournament dominated a match in which they left it late to secure the victory, having squandered a series of chances that threatened to overrun Hungary.
Belgium went for the jugular from the start, with Hazard and Kevin de Bruyne running the show during a first half in which they had 16 shots on goal, eight on target. De Bruyne could have had at least a hat-trick in the early stages but found goalkeeper Gabor Kilary in fine form.
Belgium led after ten minutes when De Bruyne swung in a free-kick from the left which was met by a powerful header by Toby Alderweireld that gave Kiraly no chance.
Hungary survived a potential avalanche before moving up a gear in the second half when Adam Pinter and Roland Juhasz went close.
But substitute Michy Batshusyi gave Belgium breathing space, converting Hazard’s perfect low cross in 78 minutes with his first touch, and one minute later, Hazard finished off a counter-attack when he surged across the edge of the penalty area and fired a low shot just inside Kiraly’s left-hand post.
The rout was complete when Yannick Carrasco broke clear on the left and rifled a low shot beyond Kirali.