Hamdi Salihi's 67th-minute strike proved to be the only goal of the contest in Oslo. The visitors were reduced to ten men in the closing stages after Andi Lila picked up two bookings in quick succession, but their opponents were unable to salvage anything from the game.
Norway, who started the day second in the group, have now dropped down two places. Albania stay third and Iceland are up to second - with both teams two points better off than the Norwegians - after their victory in Slovenia.
Salihi produced the game's first attempt on goal with a shot in the third minute that was comfortably saved by Rune Jarstein, and Tarik Elyounoussi headed wide at the other end. Migjen Basha then fired the wrong side of Jarstein's post before Elyounoussi saw an effort blocked by Armend Dallku. Seconds later John Arne Riise sent the ball over the bar left-footed from Elyounoussi's corner.
Salihi was off-target with two further shots, but following an Elyounoussi effort that went too high just before the hour mark, the Albania striker broke the deadlock with a right-footed finish into the top corner having been teed up by Ervin Bulku. After Salihi struck another attempt over, Norway pushed for the equaliser, with Tom Hogli shooting wide and Mohamed Abdellaoui bringing a fantastic parry out of Etrit Berisha.
Lila was then shown a yellow card in the 84th minute for time-wasting and another three minutes later for a foul on Abdellaoui. Riise could only send the resulting free-kick into the wall and Albania held on for all three points.