Marc Wilmots' men were far from their best once again, but it was still enough to see off the Asian nation on Thursday night
Coming into the final Group H clash, South Korea needed to beat its 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 was ultimately unable to fulfil its end of the bargain, while Belgium prepares 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 Vertonghen and goes through with a maximum of nine points, while South Korea heads home early.
Marc Wilmots insisted in the build-up that his side would not go easy on its 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 was routinely invited forward.
Hong's men lacked any creative spark, however, allowing Belgium to gain a foothold and Dries Mertens inexplicably failed to give hsi team the lead in the 25th minute as he blazed over from close range after pouncing on a loose ball.
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 its 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 it could, but Wilmots' men finally struck on the counterattack with 13 minutes to go.
Second-half substitute Divock Origi blasted a ferocious effort at Jung Sung-Ryong 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 leveled 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 it into the last 16 in high spirits.