Kyrgyzstan goalkeeper Kutman Kadyrbekov was called into action after just 12 minutes when he kept out Koo Ja-cheol's low strike.
The Dordoi Bishkek player was a busy man from then on.
Kim Min-jae broke the deadlock when he headed home a Hong Chul corner four minutes before half-time.
Hwang Ui-Jo and Hwang Hee-Chan both had chances to double Korea's lead but struck the 'woodwork'.
Paulo Bento's side secured a second straight win at the tournament, following a 1-0 victory over the Philippines in their Group C opener.
The two-time champions next face China, who currently sit top of the group on goal difference.