The stand-in captain hit the winner 12 minutes from time as Belgium finished with a perfect three wins in Group H. They now play the United States in the last 16. South Korean goalkeeper Kim Seung-Gyu could only parry a fierce shot by substitute Divock Origi and it went to the feet of Vertonghen, who buried the rebound and leapt into the crowd to celebrate.
FINAL GROUP H STANDINGS
Belgium Played 3, Won 3, Goals for 4, Goals against 1, Points 9
Algeria Played 3, Won 1, Lost 1, Drawn 1, GF 6, GA 5, Points 4
Russia Played 3, Lost 1, Drawn 2, GF 2, GA 3, Points 2
South Korea Played 3, Lost 2, Drawn 1, GF 3, GA 6, Points 1
South Korea had needed a big win to stand any chance of qualifying, and they were given hope when Steven Defour was sent off for a stamp just before half-time. But they failed to create clear-cut opportunities against an obdurate Belgian defence and depart the tournament winless, as did regional rivals Japan, Iran and Australia.
Belgium will take on USA in the next round at Salvador on July 1
Belgian coach Marc Wilmots made seven changes from the team that beat Russia 1-0, giving Manchester United 19-year-old Adnan Januzaj his World Cup debut, to keep players fresh for the knock-out stages. South Korea showed urgency at the start and they had two hopeful penalty shouts waved away before Kim Young-Gwon, receiving the ball in the area from a free-kick, disappointingly blasted off-target.
Son Heung-Min received a great through-ball but was quickly closed down. Belgium showed little threat although Kevin Mirallas, bursting on to a pass from former Everton teammate Marouane Fellaini, had a goal chalked off for offside. A Mexican wave after19 minutes indicated the crowd's thoughts were elsewhere, but Dries Mertens regained their attention when he found Mirallas in the box and then miscued wildly from close range.
It looked like Belgium would take control but Ki Sung-Yueng brought a sharp save from Thibaut Courtois with a low drive before Defour cleared Koo Ja-Cheol's header off the line from the resulting corner. The busy Mertens fired another chance well wide and then forced goalkeeper Kim Seung-Gyu to tip a free-kick over the bar after he surprised him by trying his luck from distance.