The Scandinavians have not been at their best during the first week of the Games, but battled hard for a win.
Korea, who are already knocked out, were playing without pressure and four successive goals midway through the first half gave them a 9-7 lead.
But Denmark were able to hit back and they had reduced that deficit to a single goal by half-time, with the scoreboard reading 14-13.
The Asians also started the second half strongly and opened that gap back up to three, before a golden spell from Denmark saw them haul it back and take the lead for the first time since the 12th minute after scoring five out of six goals.
They held on in the end to claim the win, with Anders Eggert Jensen and Michael Knudsen each throwing in six, a tally matched by Korea's Lee Jae Woo and Eom Hyowon.
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