Kasper Hjulmand’s side were struggling to break down a stubborn Finnish side, who were more than holding their own in the opening stages of this Nordic battle.
Jesper Lindstrom saw his speculative effort pushed over the bar by Lukas Hradecky, but chances for the visitors were thin on the ground against the organised Eagle-owls.
The Red and Whites were asking more of the questions, although Finland’s counter-attack threat was clear to see, when some enterprising play from Glen Kamara teed up Teemu Pukki, whose effort was blocked by Andreas Christensen.
The hosts would be the happier of the two sides going into the break, with their defence not breached in more than 300 minutes of qualifying action as referee Szymon Marciniak blew for the interval.
Aiming to change that with haste, Christian Eriksen was one Denmark's key instigators going forward after half-time, and the Manchester United midfielder almost broke the deadlock within five minutes of the restart, executing a wonderful free-kick that was parried away at the last moment by Hrádecký.
As the minutes ticked by, Finland remained resolute and disciplined in their defensive shape. Meanwhile, Hjulmand’s men were looking for inspiration from one Christian to another, as Hrádecký pulled off another show-stopping save to parry Nørgaard’s strike over the bar.
But just as Denmark looked set to endure a frustrating night in the Finnish capital, Højbjerg entered the fray. Several long-range efforts had failed to do the job, until the Tottenham midfielder clinically dispatched his effort into the bottom corner.
There was nothing that Hrádecký could do on this occasion, and the strike ended the hosts’ four-match winning run in Euro 2024 qualifying. It is not a game that will be remembered for its entertainment value, but the Danes will not care a jot if these three points help to take them to the European Championship finals.
Meanwhile, it was a night of frustration for Finland, who conceded only a second goal in their last eight Euro home qualifiers after Hojbjerg’s winner.
Flashscore Man of the Match: Pierre-Emile Hojbjerg (Denmark)
Montenegro left it until the 96th minute to earn themselves a priceless 2-1 victory over Bulgaria with Stevan Jovetic popping up late to earn them all three points.
Elsewhere, Moldova scored through Vadim Rata eight minutes into the second half to beat Faroe Islands.
