Jan Vertonghen swept home the winner 12 minutes from time as Kim Seung-gyu could only parry Divock Origi's drive into the path of the Belgian captain.
The win came despite the fact Belgium played the whole of the second-half with only ten men after Steven Defour was given a straight red for a two-footed lunge late in the opening period.
Belgium were virtually assured of ttopping the group before the game, but they have now progressed with a perfect nine points and will meet USA in the last 16.
South Korea's best chance to score came before the hour mark when Lee Chung-yong's cross-cum-shot hit the crossbar with Belgium goalkeeper Thibaut Courtois beaten.
The result eliminated South Korea, who had progressed past the group stages in two of the last three World Cups.
Belgium coach Marc Wilmots rested some players and made seven changes to the team that beat Russia 1-0.
Premier League performers Kevin Mirallas and Adnan Januzaj both started.
South Korea coach Hong Myung-bo made just two alterations to the side that fell 4-2 to Algeria, including Kim who replaced Jung Sung-ryong in goal.
The Europeans dominated possession but had to wait until the 25th minute to create their first real chance.
Dries Mertens should have given his side a lead when he got behind a rebound in the six-yard box but he struck his effort over the bar with only Kim left to beat.
The Taeguk Warriors almost broke the deadlock on the half-hour mark but Courtois dived to his right to clear Ki Sung-yeung's powerful drive from 30 yards.
Seconds later, Mertens made a goal-line clearance from Son Heung-min's close-range header with Courtois unable to get his hands on the ball.
Mertens, who was active at both ends of the pitch, then tested Kim with a right-footed volley from outside the area which the keeper saved.
Before the break, Australian referee Ben Williams gave Defour his marching orders after the player stamped on Kim's right shin.
The Asians made one substitution at half-time with striker Lee Keun-ho replacing Han Kook-Young.
Keun-Ho almost made an immediate impact when he headed Lee Chung-yon's cross from the right just over the bar.
Before the hour mark, Chung-yon surprised Courtois when his long-range attempt crashed off the woodwork.
Wilmots made a double substitution soon after with Nacer Chadli and Divock Origi entering the pitch.
Origi wasted little time in helping Belgium take the lead.
His right-footed shot from 20 yards was kept out by Kim but the keeper could not hold onto the ball and Vertonghen was on hand to smash the ball into the back of the net.
Despite the numerical disadvantage, Belgium held on for the win.