Iceland finished second in the group behind Switzerland who qualified automatically for the 2014 finals in Brazil.
Kolbeinn Sigthorsson put Iceland in front after 12 minutes when Tore Reginiuseen played him onside and he fired the ball past Rune Jarstein.
Daniel Braaten levelled for Norway on the half-hour, holding off a defender to slot home from close range.
Sigthorsson and Birkir Bjarnason could have put the game out of reach for the visitors in the second half but instead hundreds of Iceland fans had to wait until the final whistle to celebrate the team's achievement with the players.
- Sports & Recreation