The Scandinavians had been on course for a second win of the tournament after 11 goals from Linn Jorum Sulland had inspired them to a 27-26 lead going into the final moments.
But Republic of Korea, who had come in to the game with an 100 per cent record, ensured they remained unbeaten thanks to Ryu Eun Hee's goal with 15 seconds to go, which left Norway with no chance to respond.
Thorir Hergeirsson's side, who won one and lost one of their opening two matches, must have got out of the wrong side of bed as after 20 minutes they trailed 12-8 to slick opponents.
Two goals from Sulland before the break reduced their deficit to 15-13 at half-time and that set them up for a strong second half, in which they were able to level and then progress to a 23-20 lead by the midway point.
But Republic of Korea, who are notoriously strong at Olympic Games, never gave up and were down 27-26 going into the final minute, rescuing a point with the final act.