Second-half strikes from Kai Havertz and Jamal Musiala got the job done for Julian Nagelsmann's side, who had to overcome a brief Red and Whites storm and a literal thunderstorm in the first half.
Kasper Hjulmand's men were building up a head of steam before flashes of lightning forced a 25-minute hiatus, after which the Germans were the dominant force and thoroughly deserved their place in the last eight.
Either Spain or Georgia will be Die Mannschaft's foes in Stuttgart on July 5, while their Scandinavian counterparts head home on the back of a largely forgettable Euros campaign, especially after their magical run to the 2020 semis.
Andersen goes from potential hero to definite zero
A few moments after Joachim Andersen thought that he had opened his senior Denmark account, the Crystal Palace defender became the villain in his own penalty area during a chaotic four-minute period.
Andersen had capitalised on some chaos in the Germany box as Nagelsmann's men failed to deal with a cross, and he lashed home clinically into the bottom corner, only for a VAR review to deny him due to Thomas Delaney's offside offence.
As the hosts charged down the other end of the field, Andersen fronted up to David Raum as the RB Leipzig man delivered a cross into the box, but the ball took a nick off of his outstretched finger before sailing behind.
Following a check of the monitor, Michael Oliver pointed to the spot - where Havertz coolly dispatched Germany's opening goal - to well and truly rub salt into the centre-back's wounds.
Lightning causes chaos as Denmark momentum halted
After the early shock of Nico Schlotterbeck's disallowed goal and a barrage of German attacks, Denmark had weathered the Mannschaft storm and began to get a foothold in the game as the first half wore on.
However, one storm that neither the Danes nor the Germans could weather was a fierce series of lightning strikes and rumbles of thunder over the Signal Iduna Park, which forced referee Michael Oliver to bring proceedings to a halt.
The two sets of players briefly took refuge inside their technical areas at the downpour became heavier, hailstones descended upon the field and the lightning persisted, giving Oliver no choice but to direct playing and non-playing personnel down the tunnel.
As some fans ducked for cover, others were literally dancing in the rain before the players re-emerged for their warm-ups after around 25 minutes, and thankfully, the unforgiving downpour did not lead to the quality of the action worsening.
The Danes' momentum was well and truly killed, though, and their attempt at playing a high line proved completely fatal in the 68th minute, where Musiala raced through and calmly slotted home his third of the tournament to rubber-stamp the hosts' progression.