Defender Jan Vertonghen netted the only goal of the game 13 minutes from time to ensure the Belgians made it three wins out of three to top Group H.
READ: All the action as it happened
The first half produced little in the way of goalmouth action as neither side managed to create many clear-cut chances, but Dries Mertens did miss a sitter from about eight yards out with only the keeper to beat on 25 minutes after Kevin Mirallas' blocked shot fell kindly to him in space.
Then came what looked to be the turning point of the match when Steven Defour received his marching orders for a studs-up challenge on Shin-Wook Kim just a minute before half-time.
But Korea were unable to make their one-man advantage count in the second half against a solid Belgian defence and never looked like having quite enough in their locker to really trouble their opponents.
Belgium made sure of top spot in the group when Vertonghen followed up Divock Origi's powerful long-range effort in the 77th minute to finish past Korea goalkeeper Seung-Gyu Kim, who was unable to parry the shot away from goal.
The Europeans top the group with three wins out of three, while Algeria finish second after a 1-1 draw with Russia in the other Group H match on the night.
Belgium will play USA in the Last 16. Algeria, who secured a piece of history by ensuring the first time two African countries progressed past the group stages of the World Cup, will face Germany.