On a crackling evening in front of an expectant Glasgow crowd, substitute Kieran Tierney restored the home side's lead in the 93rd minute from outside the box.

And there was still time for a sensational fourth from fellow substitute Kenny McLean, who lifted the ball over Denmark goalkeeper Kasper Schmeichel from the halfway line.

Scotland finished as Group C winners with 13 points, two clear of Denmark, ranked 18 places above them.

The win means Steve Clarke's men will be at next year's World Cup in Canada, Mexico and the United States while Denmark, who only needed a draw to qualify automatically, face the lottery of the play-offs.

"There's always one last step," Scotland manager Steve Clarke told the BBC."And the last step is always the hardest step.

"So it was just to put their minds at ease, make them comfortable, make them know that they could handle the occasion."

Clarke was dumbfounded by the quality of his team's strikes.

"Scott McTominay scored the best overhead kick that I've ever seen," he said."And it might not have been the best goal of the night. Absolutely incredible."

Denmark's shock 2-2 draw at home to bottom side Belarus on Saturday had given the Scots an automatic qualification lifeline, despite their 3-2 defeat in Greece on the same night.

Outrageous McTominay

On an evening of high emotion and nerves at Hampden Park, Scotland took the lead in just the third minute courtesy of a phenomenal McTominay overhead kick.

With his back to goal near the penalty spot, the Napoli midfielder leapt acrobatically, firing the ball home.

The Danes quickly settled and dominated possession for the rest of the half but could not find the net.

However, Rasmus Hojlund, McTominay's Napoli teammate, levelled from the penalty spot in the 57th minute.

Four minutes later the Danes were down to 10 men when Rasmus Kristensen was harshly handed a second booking after being adjudged to have brought down John McGinn.

The Scots were back in front when Lawrence Shankland turned in a corner from Lewis Ferguson in the 78th minute only for Manchester United defender Patrick Dorgu to side-foot home minutes later to level at 2-2.

But Scotland lifted themselves again for one last push.

Tierney met a loose ball first time, curling it sweetly past Celtic's Schmeichel from 25 yards before McLean made the win certain, ending decades of pain.

"That just sums up this squad," said captain Andy Robertson."Never say die. We just keep going right to the end and one of the craziest games.

"We put the country through it, but I'm sure it's worth it. We're going to the World Cup.