Polish-born Lukas Podolski celebrated his 100th appearance for Germany with his 44th international goal to put his side in front and although Michael Krohn-Dehli's equaliser gave the Danes hope of reaching the quarter-finals, Lars Bender struck 10 minutes from time to seal a third German victory in a row.
Germany will face surprise quarter-finalists Greece in Gdansk on Friday and Denmark, despite giving a good account of themselves in the tournament, go home.
Portugal finished runners-up in the tournament's toughest group after coming from behind to beat the Netherlands 2-1.
Despite only needing a point to guarantee reaching the last eight, Joachim Loew's powerful Germany side were never going to settle for a draw and produced another efficient performance full of positive, forceful football.
While Podolski crept up the all-time list of Germany's scoring charts at the European Championship, moving joint third with Juergen Klinsmann on 15, Bender celebrated his first on his first start, clipping the ball into the corner of the net after 80 minutes.
"The most important thing is that we won," said 27-year-old Podolksi who smashed a shot past Danish goalkeeper Stephan Andersen after 19 minutes from a cross by Thomas Muller.
"It was a tough match against a strong Denmark team and fortunately we got the second goal and won it," Podolski added.
"It was something special for me that I got a goal in the 100th match and shot it with my right foot too."
With news of Portugal leading against the Dutch, a Denmark winner could have left three teams on six points but Germany left nothing to chance with Bender's late effort taking them into the quarter-finals with three group wins for the first time at the European Championship.
Krohn-Delhi, who also scored in Denmark's 1-0 win over the Netherlands, said his side could be proud of their performances.
"I am very disappointed like the rest of the team but I'm of course proud and I think we had something to offer," he said.
"We have a young team so we have a lot to work with."
