There were no football strikes to be had in the opening 45 minutes, which was impacted by the weather as a thunderstorm forced a brief postponement of the match, just as Denmark began to carve out a few chances.
However, Kasper Hjulmand's men were firmly second best in the second 45, where Kai Havertz's penalty and a fine Jamal Musiala finish ensured Die Mannschaft's progression to the last eight of the tournament, where either Spain or Georgia will meet them.
Here, Sports Mole analyses Germany's two-goal success over Denmark, including highlights, our man of the match and stats.
HIGHLIGHTS
4th min: Germany think they take the lead early. Toni Kroos's gorgeous inswinging corner to the edge of the six-yard box is hammered in by the head of Nico Schlotterbeck, but the strike is disallowed for blocking from Joshua Kimmich on Andreas Skov Olsen.
7th min: Kimmich lets fly from 20 yards and a strong fist from Schmeichel turns it over for a corner. The same combination - Kroos to Schlotterbeck - forces the Dane into another scrambling save.
10th min: Havertz beats the offside trap to meet Antonio Rudiger's lofted pass and goes for the Robin Van Persie special with a left-footed volley, which Schmeichel turns behind.
21st min: Joachim Andersen's pass over the top is met by Eriksen with a wonderful touch on the edge of the box, but the toe of Rudiger denies him.
24th min: Denmark slowly growing in confidence. Eriksen's crisp pass into Joakim Maehle opens the door for the left-back to shoot, but his effort from a tight angle grazes the side netting on its way behind.
35th min: The match is halted as thunder and lightning descend on Dortmund. Michael Oliver directs both teams off the field and eventually down the tunnel, and play is stopped for around 25 minutes as the storm passes.
37th min: A double chance for Germany right away; Havertz heads straight at Schmeichel from point-blank range, before the ball is recycled and Schlotterbeck ripples the side netting - some German fans thought he had scored.
42nd min: Schlotterbeck gets the ball caught under his feet inside his own box and is robbed by Rasmus Hojlund, but the Manchester United man can only find the side netting.
45th min: A quick Denmark break sees Eriksen and Thomas Delaney link up to set Hojlund away, but Manuel Neuer does enough to thwart him and the hosts survive.
48th min: Chaos in the Germany box results in Joachim Andersen lashing the ball home into the bottom corner, but the Crystal Palace defender is denied; a VAR review shows that Thomas Delaney was offside.
GOAL! GERMANY 1-0 DENMARK (HAVERTZ)
52nd min: Andersen's misery continues as a David Raum cross strikes his outstretched hand - albeit from close range - and Oliver awards Germany a penalty after checking the screen. Havertz steps up, stutters and places a perfect spot kick into the bottom right corner, despite Schmeichel going the right way.
59th min: An absolutely exquisite piece of skill takes Havertz away from Andersen and Jannik Vestergaard and the Arsenal man is through on goal, but his delicate dink lands just wide of Schmeichel's far post. Massive chance.
66th min: Hojbjerg sends Hojlund in with a beautiful threaded pass, but again, he snatches at his shot and it is straight into the forearms of Neuer.
GOAL: GERMANY 2-0 DENMARK (MUSIALA)
68th min: One long ball over the top from Schlotterbeck completely takes the Danish defence out of the game. Andersen is no match for Musiala in a foot race, and the Bayern Munich man strokes home his third of the tournament into the far corner with panache. 2-0.
90 +1 min: Substitute Florian Wirtz has the ball in the back of the net, but the offside flag denies him.
MAN OF THE MATCH - NICO SCHLOTTERBECK
Only starting on his regular pitch due to Jonathan Tah's suspension, Nico Schlotterbeck made an excellent case to keep his spot in the quarter-finals and beyond, despite a scare when he lost the ball to Rasmus Hojlund inside his own penalty area.
The Borussia Dortmund defender was otherwise exceptional and could count himself unfortunate to see his early header disallowed, but he provided an exquisite ball over the top for Musiala to run onto and has given Nagelsmann real food for thought. A mention for his partner Antonio Rudiger, though.
STANDOUT MOMENT
Only a few moments after he thought that he had broken his national team duck, Andersen went from hero to zero as he conceded a controversial penalty for Havertz's opening goal, although whether the spot kick should have been awarded was up for debate.
Andersen's arm was no doubt in an unnatural position when he blocked Raum's cross, but he was in extremely close proximity to the Germany left-back, not that the officials took that into account.
BEST STAT
MATCH STATS
Possession: Germany 55%-45% Denmark
Shots: Germany 15-11 Denmark
Shots on target: Germany 9-2 Denmark
Corners: Germany 6-6 Denmark
Fouls: Germany 7-15 Denmark
LINEUPS
GERMANY (4-2-3-1): Neuer; Kimmich, Rudiger, Schlotterbeck, Raum (Henrichs 80'); Andrich (Fullkrug 64'), Kroos; Sane (Anton 88), Gundogan (Can 64'), Musiala (Wirtz 80'); Havertz
DENMARK (3-4-1-2): Schmeichel; Andersen, Christensen (Bruun Larsen 81'), Vestergaard; Bah, Hojbjerg, Delaney (Norgaard 69'), Maehle; Eriksen (Kristiansen 81'); Skov Olsen (Poulsen 69'), Hojlund (Wind 81')