The win made it a maximum nine points for the Belgians, who will meet the United States of America in the last 16 in Salvador on Tuesday, while South Korea head for the exit.
The star-studded Belgians had already qualified for the next round, having beaten Algeria and Russia in their first two games, and even a draw would have been enough to claim first place and avoid Germany in the next round. However, when Defour was given a straight red for a needless, studs-up challenge on Kim Shin-wook, the game opened up for the Koreans.
But although they had plenty of possession and a series of clear chances, they were caught on the break when Belgium's excellent substitute Divock Origi struck from distance.
Goalkeeper Kim Seung-gyu palmed the ball into the path of the onrushing Vertonghen, who put it away with ease in the 78th minute.
In an even first half Dries Mertens had missed a golden chance for Belgium eight yards from goal when he shot well over, while at the other end, Ki Sung-yueng had a rasping long-range shot well saved by Thibaut Courtois in the Belgium goal.
Belgium coach Marc Wilmots made seven changes from the team that beat Russia, with captain Vincent Kompany and fellow defender Thomas Vermaelen dropping out due to slight injuries, while playmaker Eden Hazard started on the bench.