Steve Clarke's men clinched their place in Germany with two games to spare last month and, following a 2-2 draw with Georgia on Thursday night, there were thrills and spills in the final Group A game in Glasgow.
The Tartan Army were in party mood but they were silenced in the third minute of a roller-coaster first half when Aron Donnum fired the visitors ahead before Scotland captain John McGinn levelled from the spot 10 minutes later.
Norway restored their lead through striker Jorgen Larsen in the 20th minute before an own goal in the 33rd minute by visiting defender Leo Ostigard had the Scots level again.
The second half was no less open and a fine finish by midfielder Stuart Armstrong just before the hour mark put the home side ahead but Norway substitute Mohamed Elyounoussi cancelled that out in the 86th minute with a header.
Nevertheless it is Scotland and group winners Spain who qualify automatically for next summer's finals and the Scots will go into the draw as Pot 3 seeds.
It was another thrilling match in an unforgettable campaign.
Clarke reshuffled his side, with Luton striker Jacob Brown making his first start in his eighth appearance as Jack Hendry, Armstrong and Kenny McLean also came in. Ryan Porteous, Billy Gilmour, Ryan Christie and Lyndon Dykes dropped to the bench.
Stale Solbakken's side were without injured Manchester City superstar Erling Haaland, their captain and Arsenal midfielder Martin Odegaard and Sevilla goalkeeper Orjan Nyland, which on the face of it increased the home side's chance of finishing the campaign with a flourish.
The visitors, however, were keen to avenge the 2-1 defeat by Scotland in Oslo which had done so much to shape both sides' fortunes and they got off to the perfect start.
A cross into the middle from Julian Ryerson came off the foot of Larsen straight to Donnum, whose shot from 14 yards clipped Scotland defender Nathan Patterson before going past keeper Zander Clark and in off a post.
The goal stunned the home fans but they were soon cheering when referee Horatiu Fesnic pointed to the spot after judging that Callum McGregor's shot had struck the arm of Donnum inside the box.
McGinn slotted the penalty past Norway keeper Egil Selvik for his third goal of the campaign and his 18th international goal in total to tie with former Scotland striker Kenny Miller.
However, Scotland were again trailing when Larsen got a flick on Ryerson's deflected cross at the near post and the ball squirmed past Clark and spun over the line with the on-rushing Donnum making sure.
The goals kept coming and the home side were level again when Scott McTominay's whipped-in corner from the left was just missed by McLean, with the ball striking the luckless Ostigard and bouncing into the net.
Norway remained dangerous and in the 37th minute captain Patrick Berg came close with a 30-yard free-kick and minutes later only a brilliant block by Patterson denied Donnum a second goal, before Armstrong came close with a drive in the last action of the first half.
The end-to-end action continued after the break.
Brown missed a good chance from right in front of goal but only seconds before Armstrong drilled McGinn's cut-back into the net from 16 yards, after playing a one-two with his fellow midfielder.
Dykes, Christie and Lewis Ferguson soon came on for Brown, Armstrong and McLean and then Ryan Jack replaced McGinn, who had taken a knock.
By then Norway were going all out for their third goal and in the 82nd minute Clark made a good diving save from substitute Kristian Thorstvedt's header from close range.
Former Celtic attacker Elyounoussi made no mistake when burying a Ryerson cross from two yards out, however.
The Tartan Army showed their appreciation at the end of five added minutes and now all eyes are on Germany next summer.