Marc Wilmots's side netted three times in the final 12 minutes - two which involved Eden Hazard who was a threat throughout the 90 minutes - as the Red Devils made a huge statement to the teams who remain at the tournament.
Before the competition started, Belgium were tipped to have a run to the latter stages of the tournament and from the opening whistle in Toulouse, they produced the kind of football that their array of attacking players should be producing on a more regular basis.
Kevin De Bruyne was particularly lively in the first 10 minutes and he soon provided the pass that helped break the deadlock as Toby Alderweireld powered his header past Gabor Kiraly after meeting a free kick from the Manchester City playmaker.
De Bruyne almost turned goalscorer seven minutes later but his low shot was comfortably saved by Kiraly, before Hungary eventually threatened at the other end when Balazs Dzsudzsak got a shot in from distance.
Romelu Lukaku was proving a handful for the Hungary defence and a perfectly-weighted pass found the run of De Bruyne but he could not generate enough pace on his header and the chance went begging.
De Bruyne was involved in the majority of Belgium's moves but he almost doubled his nation's advantage from a 20-yard free kick but 40-year-old Kiraly defied his age to tip the ball onto the crossbar.
As half time approached, Gergo Lovrencsics and Dzsudzsak fired marginally off target before Belgium attacked the other end with Dries Mertens hitting his shot straight at Kiraly after excellent work from Hazard.
Less than a minute after the restart, Hazard nearly found a second for Belgium but after cutting inside onto his right foot, Kiraly was equal to a shot that seemed destined for the top corner.
Clear-cut opportunities were few and far between until the start of the final quarter of the contest, when Adam Pinter had a deflected effort tipped over the crossbar by Courtois before Roland Juhasz's half-volley narrowly missed the far post.
Hungary were made to rue those two near misses as Belgium secured their place in the last eight with two goals in the space of three minutes, with Hazard having a role in both goals.
Moments after being introduced by Wilmots, Michy Batshuayi was perfectly placed to convert from close range after being found by Hazard before the Chelsea playmaker made it three soon afterwards after cutting inside onto his right foot and finding the bottom corner of Kiraly's goal.
Szalai and Akos Elek came close to finding a consolation goal for Hungary but as the game entered added-on time, Yannick Carrasco was played through on goal and he made no mistake in sliding the ball past Kiraly to cap a fine performance from his side.