Yugoslavia had qualified ahead of the Danes but UEFA excluded them as the country descended into civil war.
As group runners-up and the second-placed team with the best record, Denmark were an obvious replacement.
The early stages showed little of what shocks were ahead. Having had minimal preparation, Richard Moller-Nielsen's men failed to score in their opening two group one matches - drawing 0-0 with England and going down 1-0 to host nation Sweden.
UEFA persuaded to delay 2012 choices
In the final group games Denmark would have to beat France and pray for an English defeat against Sweden. David Platt's fourth minute goal in Solna appeared to have set England on their way.
But Jan Eriksson levelled the score and Graham Taylor famously withdrew Gary Lineker as his side searched for a winner. It was a sad end to a sparkling international career; even sadder when Thomas Brolin stuck away a fantastic winner eight minutes from time.
Henrik Larsen got Denmark off to a flier in Malmö with an eighth-minute opener, only for the exceptional Jean-Pierre Papin to restore parity on the hour mark. With time running out Lars Elstrup notched the Danish winner, and it was a Scandinavian party as France and England were unceremoniously dumped out.
The Netherlands and Germany were in confident form in group two, but with the former-Soviet CIS also in contention it fell to lowly Scotland to play a deciding role.
Already eliminated, the Scots pulled out a miraculous performance to thrash the CIS 3-0 thanks to goals from McStay, McClair and McAllister.
Meanwhile the Dutch were continuing their red-hot rivalry with Germany. Victors in 1988, Holland got their comeuppance in the 1990 World Cup, This time the men in orange powered to a 3-1 win to seize cross-border bragging rights.
The last four was a bridge too far for the hosts. Against the star-studded Germans, Sweden went behind to a Thomas Hässler free kick that completely wrong-footed the hapless Thomas Ravelli.
"The game before [Hässler] scored against Russia. He had a good shot to the left of the goalkeeper. I thought he would shoot the same shot against me. He put it over the wall - and I didn't see the ball before it was too late," reflected the rueful Swedish custodian.
Karl-Heinz Riedle made it two just before the hour, and despite a late flurry of goals Berti Vogts's men held on for a 3-2 win.
Striker Jürgen Klinsmann came into the side at the injured Rudi Völler's expense, and recounts how both he and the German squad grew in confidence:
"From game to game I had more and more fun. Pass by pass I made progress.
"By the time we got to the semi-final against Sweden I was convinced that we could do it. And before the final we had a lot of self-confidence - maybe too much self-confidence."
The Netherlands, never short of self-confidence themselves, went into their semi-final against Denmark as huge favourites, but got an equally big shock in the opening minutes, when Larsen converted Brian Laudrup's cross.
A young Dennis Bergkamp hit back on 23 minutes, but once again the Danes showed enormous spirit, Larsen once again van Breukelen just after the half hour.
Holland weren't finished. Frank Rijkaard swooping to level as time ran out to take the match into a goalless extra period and penalties.
It came down to Europe's best striker against a man soon to be recognised as the continent's best goalkeeper - Van Basten against Schmeichel. The Dane saved to set up a dream final.
Ruud Gullit was certainly impressed by Schmeichel's presence: "A very powerful guy. Charismatic also. You had a feeling that there was somebody there in the goal that makes you already very strong as a team."
The final was not a classic game, but certainly provided a classic result. After 20 minutes of unbroken German onslaught - with Schmeichel once more saving the Danish bacon - the underdogs broke.
The ball fell to the unlikely figure of John Jensen and the normally goal-shy midfielder struck firmly past the unsighted Illgner.
Again Schmeichel denied Klinsmann before, with 12 minutes remaining, Kim Vilfort sealed a remarkable 2-0 win.
"A lot of people, after we actually won that trophy, said that we were probably not the best team in the tournament," playmaker Laudrup said.
"But I think: Do not underestimate a team like that. Maybe we were not playing the most fantastic football in all the games. But I think if you beat teams like Germany and Holland, obviously you deserve to get the title."
Coming up: Football comes home for Euro '96, but England's campaign ends in familiar fashion.
Ukraine puts on brave face
Platini: Ukranian cities in doubt