Patricia Augustin, 19, of Indonesia says she scours the Internet every day for the latest updates on Korean pop music. Paula Lema Aguirre, a high school student from Peru, says she is happiest when she sings Korean songs, especially “It Hurts,” the group 2NE1’s single about teenage love.

South Korean girl group Nine Muses (9 Muses) performs on stage.

Neither Ms. Augustin nor Ms. Aguirre is a native Korean speaker, but that did not stop them, along with about 40 other aspiring singers from 16 countries, from making it to the finals in December of the K-Pop World Festival competition in the South Korean town of Changwon, where they belted out Korean lyrics in front of screaming crowds packed into a stadium.