Despite being second-best for much of the game, Scotland struck the vital goal just after the hour mark, Celtic's Scott Brown latching onto a loose ball to fire low into the goal.
Norway will have been left wondering what they needed to do to breach the opposite goal, with Cardiff's David Marshall standing tall against a repeated onslaught.
Barnsley's on-loan striker Marcus Pedersen was perhaps the biggest culprit for the Scandinavians, wasting numerous chances laid on by namesake Morten Gamst, Omar Elabdellaoui and Magnus Wolff Eikrem amongst others.
Aside from the goal, Scotland's only other real chance fell to the feet of Ikechi Anya within the first 10 minutes, but his snap-shot, aside from acting as a brief respite for the visitors at the time, fell harmlessly wide of a gaping goal.
Pedersen missed a hatful of chances as Norway continued to exude confidence on the pitch, but Brown capitalised on slack finishing, slamming home on the hour mark with Scotland's only truly meaningful effort on 61 minutes.
After numerous chances went begging, Norway launched attack after attack late on in the vain hope of grabbing an equaliser as Scotland held strong.
First, Mohammed Abdellaoue found space with which to unleash an effort on the beleaguered Marshall's goal, but it was central enough for him to deal with comfortably.
Then, in the dying minutes, it was Anders Konradsen who was found on the end of the dangerous Gamst Pedersen's delivery, but the substitute snatched at the effort when he had more time.
The visitors held on to continue a fine run of form for Gordon Strachan's men, recording back-to-back away wins for the first time in over six years in the process.