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Colombia were the first to test the opposition keeper, doing so after 11 minutes when Lee Changgeun was forced to pull off a decent stop.
It proved to be a vital save as Korea took the lead just five minutes later courtesy of a Song Joo-Hoon strike.
Colombia pushed forward for an equaliser but were denied by a string of saves from Changgeun as Korea held on until half time.
The second half followed a similar pattern as the Korean keeper was by far the busier of the two, but he remained in stubborn form as he saved shot after shot from Colombia.
Colombia finally did find a way past Lee in the 89th minute, but the effort bounced back off the post as Korea survived another scare.
The South American side did finally find an equaliser in the 94th minute, however, Juan Fernando Quintero getting the goal with virtually the last kick of the match to force extra time.
Neither side could find a goal during extra time, so the match went to penalties where Song missed with Korea's second spot kick to hand Colombia the initiative.
Felipe Aguilar missed for Colombia in the next round of penalties to draw things level again before the contest entered sudden death.
Neither side let up as 11 flawless penalties followed until Colombian defender Deivy Balanta finally brought an end to the shootout with a miss that sent Korea through to the last eight.