Coming into the final Group H clash, South Korea needed to beat their European counterparts comfortably in Sao Paulo and hope that Algeria dropped points against Russia in the parallel fixture.
Russia held Algeria to a 1-1 draw, but Hong Myung-bo's side were ultimately unable to fulfil their end of the bargain, while Belgium prepare to face United States in the next round on Tuesday.
Both sides struggled to maintain control in the first period, but Thibaut Courtois was forced into action on a couple of occasions.
The Koreans were given a notable advantage towards the end of the first half as Steven Defour earned a red card, but they were unable to make the most of the dismissal despite controlling much of the second half.
Ki Sung-yeung tested Courtois from range and Son Heung-min rattled the crossbar with a fluke effort, but Belgium grabbed a late winner through Jan Vertonghen and go through with a maximum of nine points, while South Korea head home early.
Marc Wilmots insisted in the build-up that his side would not go easy on their opponents despite only needing a draw.
But the 45-year-old made seven changes from the Russia win, with Adnan Januzaj making his first international start.
The Manchester United youngster and Belgium's other attackers were exceptionally quiet in the opening stages, though, as South Korea were routinely invited forward.
Hong's men lacked any creative spark, however, allowing Belgium to gain a foothold and Dries Mertens inexplicably failed to give them the lead in the 25th minute as he blazed over from close range after pouncing on a loose ball.
South Korea eventually came to life in the final third after half-an-hour and Courtois was forced into action twice in quick succession.
The 22-year-old first denied Ki from distance and, from the resulting corner, he scrambled the ball off the line following a goalmouth melee.
Hong and his team received a significant boost to their chances just before the break as Defour received a straight red card for a callous stamp on Kim Shin-wook.
With a place in the next round slipping from their grasp, South Korea began the second half with renewed determination.
Courtois once again saved a long-range Ki attempt in the 51st minute, but the Chelsea goalkeeper had to rely on his crossbar a few moments later, as Son Heung-min's cross struck the goal frame.
South Korea took the game to Belgium as much as they could, but Wilmots' men finally punished them on the counter-attack with 13 minutes to go.
Second-half substitute Divock Origi blasted a ferocious effort at Kim Seung-gyu and, having failed to push the ball to safety, the goalkeeper was helpless on the rebound as Vertonghen smashed Belgium into the lead.
The Koreans almost levelled in stoppage time, but Courtois did well to stop Lee Keun-ho's flick at the front post and Belgium subsequently earned a third consecutive World Cup victory - sending them into the last-16 in high spirits.
