The Netherlands can also move into the last 16 on their return to a major tournament when they host Austria in Amsterdam later in the day.
De Bruyne claimed a goal and an assist with an excellent second-half display as a substitute as Roberto Martinez’s Belgium denied Denmark a crucial point in Group B.
“We can be happy,” De Bruyne told RTBF. “We knew that there would be difficult moments against Denmark and in front of this crowd, with everything that happened.”
Five days after Eriksen required emergency medical treatment to revive him in Denmark’s opening loss to Finland, his team were back in action at the same venue.
With the Inter Milan midfielder potentially within ear-shot, recovering at Rigshospitalet less than a kilometre away, the Danes took a second-minute lead to send the 25,000-strong crowd wild as Yussuf Poulsen fired into the bottom corner.
It was the second-quickest goal in European Championship history.
Belgium kicked the ball out of play after 10 minutes as the players and supporters held a minute’s applause for Eriksen, who usually wears the number 10 shirt.
The 29-year-old is to be fitted with a defibrillator after suffering a cardiac arrest.
The hosts had chances to double their lead, but the game was changed by the half-time introduction of De Bruyne for his first appearance of the tournament after suffering facial fractures in Manchester City’s Champions League final loss to Chelsea.
The midfielder showed great composure to tee up Thorgan Hazard to tap in a 55th-minute leveller, before running onto fellow substitute Eden Hazard’s clever pass and hammering a left-footed strike past Denmark goalkeeper Kasper Schmeichel with 20 minutes remaining.
“I didn’t want to celebrate that goal. I have too much respect for the Danish fans,” De Bruyne added.
Belgium join Italy in the last 16, sitting three points clear of Russia and Finland — who they face in Saint Petersburg on Monday needing a point to finish top of the Group B table.
Denmark still have a chance of reaching the next round, as a win over Russia in their final group game in Copenhagen could potentially see them through.
Frank de Boer’s Netherlands marked their return to the big stage after a seven-year absence with a 3-2 win over Ukraine in Amsterdam last weekend.
It was their first win at a European Championship since 2008 and another victory against Austria at the Johan Cruyff Arena in Group C will ensure a place in the last 16.
Juventus defender Matthijs de Ligt will reclaim his place in the side after sitting out the opener with a groin problem.
Austria on the other hand will be without Marko Arnautovic, who has been given a one-game ban by UEFA for insulting a North Macedonian player in their 3-1 win in Bucharest.
That was Austria’s first ever win at the Euro and now they too know a victory will take them through to the last 16.
Ukraine edged out North Macedonia in the group’s other game with a 2-1 victory in Bucharest as Andriy Yarmolenko and Roman Yaremchuk both scored their second goals of the tournament.
Ezgjan Alioski pulled one back for major tournament debutants North Macedonia, but they will be eliminated unless Austria beat the Dutch.
“We’re defeated but we’re not out,” said Macedonian coach Igor Angelovski.
On Friday, England look to book a ticket for the knockout phase when they welcome old rivals Scotland to Wembley, while Croatia take on the Czech Republic in the other Group D game.