Denmark had seen midfielder Christian Eriksen collapse on field in their first-up 1-0 defeat to Finland in Copenhagen and have rallied to honour their star man.
However, the Danish needed to defeat Russia and hope Finland failed to get a result against Belgium in order to seal second spot in Group B.
Remarkably, Denmark got it done in front of almost 24,000 fans at Copenhagen’s Parken Stadium, riding a wave of emotion, with Mikkel Damsgaard putting them ahead in the first half.
Yussuf Poulsen swooped on an inexplicable defensive back pass to make it 2-0 on the hour, before Russia replied with an Artem Dzyuba penalty in the 70th minute.
But Denmark added two more goals to seal their spot in the last 16, coming from Andreas Christensen and Joakim Maehle.
“What a night! We hoped that it would be a magic night at Parken,” Denmark coach Kasper Hjulmand said.
“I don’t think it would have been possible without all the support. I could feel that it really affected the players, so thank you so much for all the support. It means the world to us.
“The motivation, the team spirit and the friendship among the players were amazing. We played three games at a very high level, and if anyone deserves this, it’s our players. I can’t imagine how they managed to come back from what they went through, so a big credit to the boys.”
Meanwhile, Finland held out for more than 70 minutes before falling 2-0 to title favourites and group winners Belgium with an own goal from keeper Lukas Hradecky before Romelu Lukaku’s late strike.
Finland ends third in the group and will wait on other results to see if they progress as one of the four best-ranked third-place finishers. Russia are eliminated.