Colombia finished with nine points in Group A, ahead of France, who defeated Mali 2-0 to clinch second place with six points, with South Korea advancing as one of the best third-place teams with three points. Mali was eliminated.
Two other teams advanced on Friday to the round-of-16 knock-out stage.
Portugal defeated New Zealand 1-0 to clinch first place in Group B, ahead of Cameroon in second on four points after a 1-0 victory over Uruguay . The loss eliminated Uruguay, a nation that had become accustomed to tournament success in recent times.
Group play will wrap up on Saturday with Australia facing Spain and Ecuador playing Costa Rica in Group C. In Group D, Saudi Arabia will play Nigeria to decide first and second, while Croatia is against Guatemala.
Luis Muriel scored for Colombia in the 37th minute. Muriel's goal came after a mistake by South Korea keeper No Dong-geon, who raced off his line for a loose ball in the area, but was beaten to it by Muriel who recovered and scored into the empty net with No stranded.
''My idea is to keep scoring goals,'' Muriel said. ''This is my motivation.''
Colombia attacked throughout the first half with South Korea trying to defend and counterattack. Muriel also hit the crossbar with a rising shot from 20 meters (yards), which came just minutes before he finally broke through.
There were fewer shots in the second half with South Korea perhaps worn down by the altitude in Bogota of 2,600 meters (8,600 feet). Even the home fans, who have deafening every match with their vuvuzelas and non-stop cheering, were relatively quiet in the second half with both teams seeming to settle for the result.
''Korea was the most difficult team we have played,'' Colombia coach Eduardo Lara said. ''That's what the players said. They could not find much space but fortunately we got a goal.''
Cedric Bakambu and Alexandre Lacazette scored second-half goals as France defeated 10-man Mali 2-0.
Bakambu found the net with a right-footed shot into the far corner in the 70th minute - a minute after Mali had a man sent off - and Lacazette sealed the victory with a sharp-angled shot from the right in the 77th.
Mali played a man down from the 69th after defender Mohamed Konate received a second yellow card.
In Group B, Mario Rui scored in the first half to give Portugal a 1-0 win over New Zealand. Rui netted in the 31st minute, taking advantage of a well-timed through ball by striker Nelson Oliveira. Rui got in front of the New Zealand defenders inside the penalty area and placed a low left-footed shot into the far corner.
Emmanuel Mbongo scored in the 28th minute for Cameroon against Uruguay, whose junior team could not match the impressive run of the senior team, which won the Copa America last month and reached the World Cup semifinals last year.
''The elimination is very painful,'' Uruguay coach Juan Verzeri said. ''The plan was to reach the last 16. ... The early goal by Cameroon had an impact on us, and later - unfortunately - we could not find a goal.''
Stephen Wade can be reached at http://twitter.com/StephenWadeAP