The match at the Parken Stadium in Copenhagen was suspended shortly before half-time after Inter midfielder Eriksen collapsed to the ground with no one around him.
Team-mates and referee Anthony Taylor called for immediate help from medical staff, with the players forming a protective barrier around Eriksen while efforts were made to resuscitate him.
The 29-year-old was carried from the pitch, but positive news followed with the Danish Football Union stating Eriksen was "awake" and set for "further examinations" after being taken to hospital.
Both sets of players decided to resume the game after more than 100 minutes away from the pitch, with Joel Pohjanpalo sealing an historic triumph for Finland shortly before the hour mark against an understandably deflated Denmark side, who missed a late penalty through Pierre-Emile Hojbjerg.
Denmark started on the front foot, with Jonas Wind, Hojbjerg and Eriksen forcing Lukas Hradecky into saves inside the opening 20 minutes.
Thomas Delaney and Martin Braithwaite then fired off target as Denmark continued to push forward in search of an opener.
The game was suspended for almost two hours following Eriksen's collapse, the players ultimately returning to finish the remaining few minutes of the first half before a short half-time interval.
Despite Denmark's dominance, it was Finland who opened the scoring with their first attempt on goal, Pohjanpalo heading through the weak hands of Kasper Schmeichel in the 59th minute.
Kasper Hjulmand's side had a golden opportunity to draw level 16 minutes from full-time when Paulus Arajuuri brought down Yussuf Poulsen in the penalty area, but Hojbjerg's tame spot-kick was kept out by Hradecky.
What does it mean? Finland's famous win will soon be forgotten
Ordinarily, Finland beating a side 44 places above them in the world rankings in their first-ever European Championship match would be a head-turning result.
As it is, the win – achieved thanks to Finland's solitary effort on goal – will largely be forgotten following the distressing scenes involving Eriksen.
The reports coming out of Denmark on Eriksen's condition while his team-mates played out the game were encouraging and their attention will now surely turn to his recovery rather than dwelling on an opening-day defeat.
Hradecky thwarts dominant Denmark
Bayer Leverkusen goalkeeper Hradecky made six saves to deny Denmark, the most important of which was to keep out Hojbjerg's penalty. That save meant he became only the third goalkeeper to save a penalty on their debut appearance in the European Championship after Przemyslaw Tyton in 2012 (for Poland against Greece) and Trols Rasmussen in 1988 (for Denmark against Spain).
Hojbjerg's spot-kick woe
Hojbjerg made more successful passes (78) than any player on the pitch and his 11 possession gains was only bettered by Daniel Wass (12), but the Tottenham midfielder was unable to net from the spot and secure what would have been an emotional point for his side.
Key Opta Facts:
- Finland have only lost one of their last eight competitive matches, picking up five victories and four clean sheets in the process (D2).
- Denmark have missed three of their last four penalties in major competitions (World Cup + Euros), having scored the previous five between 1984 and 1998.
- They have also failed to win eight of their nine opening matches at the European Championships (D3 L5).
- Pohjanpalo scored Finland's first ever goal at the European Championships with what was their first shot in the competition.
- He scored his 10th goal for Finland in what was his 43rd cap for his country – becoming one of only two players in their Euro 2020 squad to have netted 10+ goals for the national side (also Teemu Pukki, 30).
- Hradecky is only the third keeper to save a penalty on their debut appearance in the European Championships after Przemyslaw Tyton in 2012 (Poland v Greece) and Trols Rasmussen in 1988 (Denmark v Spain).
Denmark face Group B heavyweights Belgium in Copenhagen on Thursday, while Finland take on Russia in St. Petersburg a day earlier.