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.
South Korea 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 off 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.
What does it mean? South Korea march on despite failing to sparkle
The 2-1 defeat to Australia in the 2015 final was the last time South Korea conceded a goal at the Asian Cup, and their defence again looked reasonably resolute until Al Romaihi's shock leveller.
That said, this was not a particularly inspired performance, especially in attack, where Son seemed to become isolated as a roving number 10. They may need more from their star man in the last eight.
This was only Bahrain's second appearance in the knockouts in the last six tournaments, but they can be proud of the performance they delivered, even if they fell just short.
Al Hayam a powerhouse
Goalkeeper Alawi may have had a much busier outing were it not for centre-back Al Hayam, who made more clearances (12) than any other player on the pitch. He deserved to see Hwang Ui-jo spurn a late chance in normal time that came from his error.
Son fails to shine
Expectations were high on Tottenham star Son Heung-min ahead of his second outing of the tournament, but he looked a long way from his explosive best in a tepid South Korean attack.
South Korea will meet the winner of the match between Qatar and Iraq later on Tuesday. The quarter-final will take place at Zayed Sports City Stadium on Friday.