The tie then went to extra-time and neither side could muster a winning goal, so the match headed to a penalty shoot-out.
Graham Gartland missed Drogheda's first spot-kick, however Alex Valencia saw his effort saved by Drogheda goalkeeper Dan Connor.
With the tie level at 4-4 after the regulation five penalty kicks per side, the tie was decided in sudden death.
All of the remaining penalty takers - including both goalkeepers - converted to leave the match tied at 10-10.
Gartland then stepped up to take his second kick of the evening and missed once more, which opened the door for the Norwegians to qualify for the next round when Stefan Barlin converted.