Marc Wilmot's men secured their first quarterfinal place at the Euros since 1980 with one of the most impressive displays in France. They will take on Gareth Bale's Wales on Friday evening for a place in the last-four.
A late goal from Yannick Carrasco capped off a perfect night for Belgium and helped them to progress to the quarterfinals of the European Championship.
The Red Devils, beaten finalists in 1980, struck first through Toby Alderweireld, but had to wait until the last quarter of an hour before finishing the job. Just minutes after coming off the bench, Michy Batshuayi tapped home the second after a short cross from Eden Hazard. A minute later, Hazard slalomed into space and curled home a brilliant goal.
But Belgium weren't finished there and Atletico Madrid's Carrasco beat the offside trap and finished beyond Kiraly, his first international goal.
Hungary coach Bernd Storck was forced to shuffle his pack at the last minute when Werder Bremen's Laszlo Kleinheisler sustained an injury in the warm-up. The lively midfielder, one of the most important players in the squad, was replaced by Adam Pinter, meaning Storck's side were slower in the defensive transition as a result.
The Belgians, with one of the most talent-rich squads in the competition, took full advantage from the start. Kevin De Bruyne was the creator for the goal on nine minutes, delivering a dangerous free-kick into the box for Alderweireld to head past Kiraly.
Five minutes later, the former Wolfsburg attacking-midfielder collected the ball in the area, but was denied by the feet of the Hungarian keeper.
Hungary, who qualified for the tournament after a playoff win over Norway, have been one of the more unpredictable teams in the tournament so far. Returning to the European Championship for the first time in 44 years, Storck's side have coped well, beating the much-fancied Austria before drawing with Iceland and Portugal.
But this was Hungary's weakest performance of the Euros. Attacking menace was limited with Adam Szalai being marshaled well by the Belgian defense. On 23 minutes, captain Balazs Dzsudzsak killed a bouncing ball on the edge of the penalty area before cracking the ball wide, forcing Thibaut Courtois to scramble across his line.
Belgium continued to hold most of the possession and De Bruyne's effort crashed against the crossbar with 10 minutes left in the half. Dries Mertens should have scored on 43 minutes, but was bettered by the veteran Kiraly.
The second half presented the Hungarians with their best spell of the game, creating a number of promising openings. Szalai sent a header inches wide of the Belgium goal and Adam Pinter charged out of midfield and forced an excellent save from Courtois on 65 minutes. Two minutes later, center-back Roland Juhasz drilled a tantalizing ball across goal, but there were no takers with the goal beckoning.
The 22-year-old Marseille striker Batshuayi is highly-regarded in French football and has attracted recent interest from West Ham after scoring 17 league goals last season. Hazard teed up the substitute on 78 minutes for a simple finish with his first touch of the game to make the game safe for the Belgians.
Two minutes later, Hazard produced a moment of great skill, dribbling past a handful of defenders and then accurately finding the bottom corner. Substitute Carrasco of Atletico Madrid used his pace to great effect to score a fourth in the first minute of stoppage time.