Norway went into the game with a 6-4 record against the Danes at the World Championship, although the Danes won the most recent clash between the two nations, last year, en route to the bronze-medal game.
Michael Brandsegg-Nygard scored just 13 seconds into overtime to give Norway a 4-3 win.
The match was off to a very slow start in the first period, but Norway did manage to get the opening goal midway through the period when Tinus Luc Koblar scored on a rebound when the puck dropped at his feet.
The Danes managed to restore parity at 7:53 when Norwegian goalkeeper Henrik Haukeland had trouble with a long shot, allowing Joachim Blichfeld to push it over the goal line.
However, Norway quickly responded with two goals in succession as Captain Andreas Martinsen made it 2-1 on a power play at 10:42 before Koblar got his second of the night three and a half minutes later.
Just 62 seconds later, however, Denmark made it a 3-2 game on a power play when Blichfeld doubled his tally of the night.
Norway clung to their 3-2 lead as time wound down in the third period, but with goalie Nicolaj Henriksen on the bench, the Danes managed to level the game with 1.1 seconds left in the game as Patrick Russell tipped it in to send the game to extra time.