Heading into the closing five minutes, Scotland were heading towards a deserved defeat with Erling Braut Haaland's penalty proving to be the difference.
However, as soon as the Manchester City forward was withdrawn, the Tartan Army threw men forward and got their reward through goals from Lyndon Dykes and Kenny McLean.
Scotland now sit eight points clear of Norway - the team deemed to be their direct rivals for qualification for Euro 2024 - with five games left, Steve Clarke's side also six points clear of Spain who have played a game fewer.
After a relatively quiet start in terms of goalmouth action, Norway should have gone ahead in the 14th minute when Alexander Sorloth rose highest to meet a cross, only for his header to go straight at goalkeeper Angus Gunn.
Scotland could be pleased with how they had dealt with Haaland during the opening 45 minutes, the forward effectively left to feed off scraps yet while remaining as a threat.
Both teams had their chances soon after the restart, Ola Solbakken failing to trouble Gunn with a weak curling effort and John McGinn hitting a shot at the other end straight at Orjan Nyland.
However, Norway got their noses in front just after the hour mark, Haaland producing a perfect penalty into the corner after Ryan Porteous had illegally held him inside the area.
As the game entered the final quarter, Sorloth just missed finding the far corner, helped by a deflection off Liam Cooper, and Scotland were left struggling to make any inroads in their search for an equaliser.
That soon changed, though, with Dykes initially getting Scotland back on level terms as he poked the ball past Nyland from just inside the area after it had somehow rolled into his path.
Scotland's travelling supporters were ecstatic and would have gratefully accepted a share of the spoils, yet less than two minutes later, their team were ahead.
While there was a touch of fortune about the leveller, the winner was sensational, McGinn and Dykes combining to tee up McLean to sweep a wonderful finish into the far bottom corner.
Although the magnitude of that strike is yet to become apparent, Norway may already be at the point of no return, collecting just one point from their opening three games, whereas Scotland can move ever closer to a second successive European Championship appearance if they can beat Georgia at Hampden Park on Tuesday.