The 29-year-old midfielder Eriksen collapsed towards the end of the first half and was given CPR by medics as his team mates formed a ring around him, before he was carried off on a stretcher and both teams left the pitch.
The game was stopped for one hour and 45 minutes but resumed after the Danish Football Association announced that Eriksen was awake and stable in hospital and both sets of players told soccer's European governing body UEFA they wanted to continue.
The game restarted and the last five minutes of the first half were played. Halftime was shortened to five minutes before play resumed again, as did Denmark's dominance of the match.
The Finns appeared to suffer stage fright in their first appearance at the finals of a major tournament, dropping to five at the back to try to snuff out Denmark's intricate passing and relying on winning free kicks to get some breathing space.
Denmark's Yussuf Poulsen won a penalty when he went down under slight contact in the 73rd minute and midfielder Pierre Emil Hojbjerg stepped up to take the spot kick, but Lucas Hradecky got down smartly to save.
In all, the hosts had 22 efforts on goal but could not make them count as Hradecky and his defence performed heroically to keep them out until the final whistle.
AS the Danes trudged dejectedly off the field, the Finnish players celebrated with their ecstatic fans, but ultimately it was a night when football did not matter with Eriksen being treated at a hospital about one kilometre away.