The Colombians just had to hold on after their two first-half goals and their pressing attack did not give their opponents any reprieve.
But the first real chance of the game came in the 28th minute when a shot in the box struck Shim Seo-Yeon.
Catalina Usme, the all-time top Colombian goal scorer, converted from the spot, sending the goalkeeper the wrong way.
The goal lifted the confidence of the Colombians with the second coming only eight minutes later through Real Madrid’s 18-year-old Linda Caicedo after a mistake from the South Korean goalkeeper, the shot from outside the box slipping through the hands of the outstretched Yoon Young-Guel.
South Korean teenager Casey Phair made history by being the youngest woman to play in the world cup at just 16.
Colombia are second in their group behind Germany who beat Morocco 6-0 in Melbourne.