It is a result which means the country have won their last six competitive matches for the first time since 1930 and ensures Scotland will have a home tie for the play-off semi-final in the bid to reach Qatar 2022.
How do the play-offs work?
The six countries who have the best runners-up record from the group stage are seeded for the first play-off match. The other four runners-up, plus the two qualifiers from the Nations League, are unseeded.
In turn, the twelve teams will be split into three play-off paths consisting of four teams.
The seeded teams will get home ties for the semi-final and then a random draw will decide which team hosts the final.
What does the win over Denmark mean?
The win has secured Scotland a place amongst the seeds and a home tie at a sold-out Hampden Park for the semi-final on March 24 or 25 next year.
Who could Scotland face in the play-offs?
Their seeded status means Scotland already know they will avoid fellow top seeds Italy, Portugal, Russia, Sweden and Wales in that opening game.
Possible opponents include Poland, North Macedonia, Turkey, Ukraine, Austria or Czech Republic, who are all unseeded for the play-off semi-final.
Home advantage for the unseeded play-off final ties on March 28 and 29 will be determined by the outcome of the draw which takes place at Fifa headquarters in Zurich on November 26.
When are the play-offs?
The semi-finals will take place on March 24–25 with the finals scheduled for March 28–29.
The three winners will join the ten group winners at the World Cup in Qatar which begins November 21.