Yussuf Poulsen's strike in the second minute helped the Danes to a surprising early lead, but a sensational Kevin De Bruyne came off the bench to set up one goal and score another to put Belgium into the knockout stage in a match marked by touching tributes to Denmark midfielder Christian Eriksen.
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The teams stopped for a minute's applause as a tribute to Eriksen, who suffered a cardiac arrest in the Danes' opener against Finland at the Parken Stadium.
As the stadium match clock showed minute 10 -- Eriksen's shirt number -- Belgium's Dries Mertens brought play to a halt and the players applauded as the Danish crowd unfurled a banner saying: "All of Denmark is with you Christian."
Eriksen is recovering at a nearby hospital and will have an implantable cardioverter defibrillator (ICD) fitted to regulate his heart rhythm. His future in the game remains in doubt.
Eriksen's collapse shocked millions of viewers around the globe. The Finland game was suspended and when it eventually resumed, the Danes lost 1-0.
The red-and-white clad fans in the 25,000-strong crowd on Thursday gave the Danish players a warm welcome as they came out before the game, and Belgian fans held up a banner saying "Belgium loves you Christian" before kickoff.
That display was topped when a giant Denmark shirt featuring Eriksen's name and number was revealed during the opening ceremony to the jubilation of the crowd, followed by a rendition of "You'll Never Walk Alone."
The gestures continued with a lusty rendition of the Danish national anthem before Denmark team captain Simon Kjaer was presented with a signed Belgium shirt featuring Eriksen's name and number by Jan Verthongen.
Once the game started, Denmark wasted little time taking the lead through Poulsen, who rolled his right-footed shot into the far corner after Danish pressure forced a giveaway outside of the Belgium box.
Belgium equalised in the 54th minute when second-half substitute De Bruyne latched onto a Romelu Lukaku pull-back, let two charging defenders slide by and calmly found an unmarked Thorgan Hazard to thumped home from close range.
De Bruyne sealed the points with another brilliant piece of play 16 minutes later. The Manchester City midfielder raced onto a layoff from substitute Eden Hazard and beat Denmark goalkeeper Kasper Schmeichel to the near post with an stoppable low strike with his left foot.
"The fans created an incredible atmosphere. The fans gave the home team a one-goal lead and at that point we were a little bit shell-shocked," Belgium manager Roberto Martinez told reporters after the match.
"It took us probably 20 minutes to start being ourselves again but we couldn't get that desire, heart and pressure that the Danish team had. I felt that in the first half, there was a lot of emotion involved.
"The second half was totally rational, we showed incredible character, big hearts and [played] with a real idea of what to do. This is the victory that you enjoy and treasure, it makes you better as a team."
De Bruyne was playing his first match since he went off injured in last month's Champions League final and Martinez praised the City midfielder who has recovered from a double facial fracture.
"You never doubt his talent. Obviously, it's a big ask to come on half-time and be able to affect the game the way he did," Martinez said.
"The way he played in the second half, he didn't look like a player that has been through surgery and has been away from the football pitch. It shows you the way he looked after himself, the way he was focused in training.
"This was a very impressive way for a player away for a long time to introduce himself and affect the game in that way."
The result leaves Denmark with zero points from two opening group games. They will play their final match against Russia on Monday with a chance to still qualify if they win and get some help in the other group game between Belgium and Finland.
Denmark coach Kasper Hjulmand said his side are eager to ensure they can prolong their stay in the tournament.
"With Christian in our minds and our hearts, we know that he's still here, we know it's going to be a tough few weeks for you Christian, we're here for you," Hjulmand told a media conference.
"We're going to stick together and we're gonna beat the Russians, we're not done in this competition."
Eriksen passed on his congratulations to the team when they returned to the dressing room, striker Martin Braithwaite said.
"He sent us a message in the WhatsApp group. I think he said that we were really awesome, I haven't had time to look, but there was a message when we entered the dressing room," Braithwaite said.
Information from Reuters was used in this report.