Belgium now faces the United States on Tuesday at 3 p.m.
Belgium made seven changes from the team that beat Russia to secure their progress and, though Dries Mertens fired their best chance over, were in cruise control until Steven Defour was sent off for a two-footed lunge at Kim Shin-wook just before halftime.
South Korea, needing a win for any chance to progress from Group H, eventually built momentum against their outnumbered rivals but rarely looked like scoring and were caught out in the 78th-minute when Vertonghen banged in the rebound after Divock Origi's shot was parried by goalkeeper Kim Seung-gyu.
Belgium top the group on nine points and will play Group G runners up the United States, while Algeria drew 1-1 with Russia to take second spot on four and earn a meeting with Germany
