The 10-man Danes looked set to head to North America with the game level in stoppage time until Tierney fired a superb strike from the edge of the penalty area to put them 3-2 ahead.
Kenny McLean sealed the win when he caught Kasper Schmeichel off his line and lobbed the keeper from miles away to secure top spot in Group C.
Scotland seals World Cup spot, Wales on their way to play-offs
Meanwhile, Wales defeated North Macedonia 7-1 in Cardiff to overtake their Group J rivals on the final matchday and finish second.
The Dragons quickly took the lead with two goals after a penalty from Harry Wilson and a goal from David Brooks.
The Macedonians halved the deficit almost immediately, but Craig Bellamy’s men hit back with a vengeance. Wilson finished with a hat-trick, including a second penalty, while Brennan Johnson, Daniel James and Nathan Broadhead also got on the scoresheet.
Regardless of the final result, Wales would have qualified for the play-offs thanks to their performances in the UEFA Nations League, but now they find themselves in pot two instead of pot four.
16 teams will take part in the play-off draw, which will take place in Switzerland on Thursday at 12 noon. The mini-tournament consists of a semi-final and a final; each round is a single stage.
Wales will play the semi-final at home against Albania, Bosnia and Herzegovina, Kosovo or the Republic of Ireland. The play-offs will take place in March next year.
Read – Five of the greatest footballers who have never played in a World Cup
See also – When are the World Cup qualifying play-offs?
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