Finland will now meet Denmark at Saint Petersburg's Yubileiny Arena in Thursday's early quarter-final, marking only the second time that the Danes have made it this far at the world hockey championships.
Denmark goalie Sebastian Dahm told TV2 Sport that the team's performance at this years' IIHF world championships is a sign that the Danes "have taken a step up in the global hierarchy".
"This is so huge for all of us and it is fantastic for Danish ice hockey. To get four wins in the world championships and make it to the quarter finals is unbelievable. I can hardly put words to it," he said.
Denmark qualified for the quarter-finals after the Czech Republic battled back from a goal down to edge Switzerland 5-4 and seal top spot in Group A. That win, combined with Danish victories over Latvia and Kazakhstan, allowed Denmark to finish fourth in the group.
Now the Danes will try to stop Finland from claiming their first medal since 2014.
The Finns expect a tough match on Thursday against the Danes, who managed to upset Group A winners the Czech Republic 2-1 on their way to the play-offs.
"Denmark are strong team," Finland forward Aleksandr Barkov said.
"They have three NHL forwards in their roster. No doubts they will battle tough but we're also intending to win. I expect an interesting game."
When these teams last met at the 2014 world championship, Finland won 3-2. That year, Finland finished as runners-up.
The Czechs will face the United States, who finished fourth in Group B despite a 3-2 defeat at the hands of Slovakia in overtime.
The other quarter final games will see Sweden take on Canada, while hosts Russia will face off against Germany.