Defender John Souttar, a late call-up and playing for the first time since he was sent off against Israel three years ago, raised the roof at Hampden Park with a headed opener in the 35th minute for his first international goal.
The tension was racked up after the break but the tenacious Scots already assured of second place, held the Danes at bay before striker Che Adams scored a late second to ensure Steve Clarke’s side will be seeded and at home for the first play-off game next March.
It was Denmark’s first defeat after nine section wins but Scotland’s sixth successive win which took them to 23 points – with just one defeat in Copenhagen – and how the Tartan Army enjoyed the performance and result.
Scotland’s 2-0 win in Moldova on Friday night meant a fifth successive victory within 90 minutes for the first time since 2007 and confidence was high.
Defender Nathan Patterson dropped out through suspension and his place was taken by Stephen O’Donnell, with attacker Ryan Christie in for Stuart Armstrong, while Souttar, took over from Jack Hendry to sighs of relief from the Tartan Army.
Captain Andy Robertson, John McGinn Billy Gilmour, Adams and O’Donnell were all one yellow card away from suspension but any fears proved unfounded on a famous night.
Kasper Hjulmand’s side started hesitantly as the Scots harried and hassled, although a cross from Rasmus Kristensen was knocked wide by the onrushing Daniel Wass.
Back came Scotland and in the 22nd minute Denmark goalkeeper Kasper Schmeichel produced a fine reaction save, using his foot to prevent Adams’ close-range shot sneaking inside the post.
Midfielder John McGinn had a shot blocked by defender Joakim Maehle before his corner was cleared away in desperation by Schmeichel and Andreas Evald Cornelius as it threatened to creep in at the near post.
Then, in a Scotland breakaway led by Robertson and Adams, the latter had a shot blocked by captain Simon Kjaer.
However, it was from another McGinn corner that the home side took the lead, with Liam Cooper rising at the back post to head back across goal for fellow defender Souttar – winning his fourth cap – to knock in from six yards.
Denmark came out after the break determined to equalise and Gordon made a great save from a Cornelius header, although the offside flag eventually went up.
However, the Scots posed problems of their own and midfielder Billy Gilmour tested Schmeichel with a looping drive from 30 yards before Adams struck the post – although again the offside flag went up.
Moments later, Robertson’s speculative effort from 45 yards clipped the top of the bar.
Kenny McLean replaced Gilmour in the 75th minute and soon afterwards Robertson and Christie made way for Scott McKenna and Armstrong as Clarke looked for fresh legs to hold back the Danes, who used all five substitutes to help increase the pressure.
In the 86th minute Gordon saved a long-range shot from Andreas Skov Olsen but again the Scots repelled the corner.
The pressure was then eased. In a wonderful break, Armstrong sent Adams racing clear and this time he slotted past Schmeichel to make it 2-0 – to the delight of most inside Hampden.
Full-back Tony Ralston came on for Kieran Tierney to make his debut before Scotland almost made it 3-0, with Kjaer blocking a goalbound shot from Armstrong.
However, the two goals were more than enough on a memorable night as the quest to reach Qatar goes on for Clarke and his team.
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