Kasper Hjulmand's team sealed second in the group despite losing their first two matches
Denmark made European Championship history by progressing to the knockout rounds with a 4-1 win against Russia on Monday.
Mikkel Damsgaard, Yussuf Poulsen, Andreas Christensen and Joakim Maehle were among the goals, while Artem Dzyuba converted a penalty for Russia.
With Finland losing to Belgium in the other game in Group B, Denmark were able to secure second place because of their superior goal difference.
What record did Denmark set?
It marks an incredible comeback for Kasper Hjulmand's team after they suffered defeats to Finland and Russia earlier in the competition.
This is the first time a team has ever survived the group stage despite losing their first two matches.
It was an unusually prolific day out for the Danes, too, as it is the first time they have scored four or more goals in a major tournament game since they beat Nigeria 4-1 in the 1998 World Cup.
The feat is made all the more impressive by the players overcoming the shock of Christian Eriksen's cardiac arrest during the clash with Finland.
Christensen paid tribute to the attacking midfielder as he celebrated his goal by holding up his hands to display Eriksen's shirt number.
Damsgaard delights Denmark
Damsgaard opened the scoring for Denmark with an excellent effort from outside the box.
At 20 years and 353 days old he is now youngest player to score in a major tournament for the country.
He is also the first Denmark player to score a goal from outside the box at a major tournament since Jon Dahl Tomasson did it against Sweden at Euro 2004.