The evening's other game saw Belarus beaten 3-0 by Group A winners Switzerland, but the Danes' unexpected loss meant they failed to capitalise and missed out on a place in the semi-finals.
The results mean Switzerland top Group A with three wins while Belarus edge through in second despite finishing level on three points with third-place Iceland and Denmark, who finish bottom.
Georgi Kondratiev's side celebrated a spot in the last four courtesy of a better head-to-head record over Iceland having claimed a 2-0 victory over them in the tournament opener.

Iceland struck twice in two second-half minutes through Kolbeinn Sigthorsson and Birkir Bjarnason to stun the home crowd.
Bashkim Kadrii pulled one back for Denmark before Hjortur Valgardsson netted a stunning injury-time strike, but it was not enough for either side as both crashed out.
The impressive Swiss made it three wins out of three thanks to a brace from Admir Mehmedi.
Mehmedi bagged his fourth goal in seven games from the penalty spot early on after Innocent Emeghara was brought crashing down by a clumsy challenge from Oleg Veretilo.
And the FC Zurich striker was on target again two minutes before the interval when a poor pass from Egor Filipenko was punished by Mehmedi, lashing home from just outside the area.
Belarus were reduced to 10-men in the second half when Sergei Matveichik was booked twice for poor tackles on the influential Xherdan Shaqiri.
And the Swiss secured a comfortable victory three minutes into stoppage time when Frank Feltscher drilled the ball past goalkeeper Aleksandr Gutor from an acute angle.