Kim Jin-su's header in the second minute of injury-time at the end of the game's first extra period was enough to deny Bahrain a famous win over a side ranked 60 places above them in FIFA's global standings.
Mohamed Al Romaihi had cancelled out a goal from Hwang Hee-chan to force the additional 30 minutes at Rashid Stadium, but Kim Jin-su met Lee Yong's cross to settle a tense last-16 encounter.
Korea Republic dominated the early possession, but it was a stinging strike from Mohamed Marhoon that threatened to break the deadlock in the opening minutes.
Paulo Bento's side were struggling to find a way through a resilient Bahrain defence, but they finally struck two minutes before half-time, when Hwang Hee-chan side-footed home after goalkeeper Sayed Shubbar Alawi had blocked Lee Yong's cross at the left-hand post.
Bahrain remained a sporadic threat on the break and it took a fine one-handed save from Kim Seung-gyu to keep out Jamal Rashed's curling strike, but they drew level with 14 minutes to go, Al Romaihi firing high into the net after Hong Chul blocked Mahdi Alhumaidan's goalbound effort into his path.
Hwang Ui-jo was gifted a chance to win the match in injury-time after Waleed Al Hayam's error, but he scuffed his effort wide of the right-hand post with only the goalkeeper to beat.
An emotional Alawi was taken from the field on a stretcher in the first half of extra-time, having failed to recover from an injury sustained while taking a goal kick, and replacement Abdulkarim Fardan could do nothing to stop Kim Jin-su securing a place in the last eight.
