The Danes went 2-0 up through Mikkel Damsgaard’s stunning 38th-minute strike and a finish just before the hour mark from Yussuf Poulsen who punished a mistake by Roman Zobnin.
Russia replied with Artem Dzyuba’s 70th-minute penalty before strikes from Andreas Christensen in the 79th minute and Joakim Maehle three minutes later wrapped up a thumping win for the hosts in front of a jubilant Parken Stadium crowd.
The result, combined with Belgium’s 2-0 win over Finland saw Hjulmand’s men claim second spot in Group B, setting up a clash with Wales in Amsterdam on Saturday.
It has been some turnaround for Denmark in their emotional campaign at the tournament, having lost their first two matches, at the same venue, after the shock of midfielder Christian Eriksen’s cardiac arrest in their opener against Finland.
Hjulmand said at his post-match press conference on Monday: “What a night. We hoped it would be a magic night at Parken.
“I want to start by saying thankyou to all the people who have been supporting us, and have shown so much love. I don’t think it would have been possible without all the support. I could feel that it really affected the players, so thankyou so much for all the support. It means the world to us.
“The motivation, the team spirit, the friendship among the players was amazing. We played three games on a very high level and if someone deserves this it’s our players. I can’t imagine how they managed to come back from what they went through, so a big credit to the boys, and thanks a lot for the support we’ve got from the whole of Denmark.
“I have to say the team and the team sprit we have and how everyone contributed was amazing.
“It’s hard to describe what this team has been through the past four weeks. We are thinking about Christian all the way.”
Asked how he himself had managed, Hjulmand said: “I manage because I have a great team around me, I have great staff, great people around me, great players.
“I think the only way I can tell it is that we are a unit. It’s not one person, it’s a unit. We are backing each other up and that is the best with Denmark, I think it is the best values we can show the world – that we stand united, we are helping each other.”
Hjulmand added regarding the last-16 tie: “Wales are a very tough opponent. They came very far last time, they have real great players, so I think it is going to be a very equal game.”
While Denmark moved from bottom before the game to second place, the opposite happened to Russia as three teams in the pool finished on three points.
Following his side’s exit as the group’s bottom team, Russia boss Stanislav Cherchesov said: “The game didn’t work as well as we were hoping.
“We had a plan. We had a few good moments when we could have scored and could have turned the game around but we didn’t score.
“Our players were ready for the game but it didn’t work in our favour. We have to analyse everything calmly to see what went wrong.”