Hosts Germany needed a second-half Kai Havertz penalty and a Jamal Musiala goal to get past Denmark 2-0 in a storm-and-VAR-dominated Euro 2024 last-16 clash on Saturday.
It was a first knock-out win in eight years for Germany, who on Friday now face the winners of Sunday's game between three-times champions Spain and tournament debutants Georgia.
"I believe we played a super game," Germany defender Nico Schlotterbeck told ZDF. "I'm so happy for the team, it's a reward for our hard work. We're playing with euphoria and with fun."
The game was suspended for 30 minutes in the first half due to a huge thunderstorm after Germany had the lion's share of the early chances.
But in the second half, Joachim Andersen thought he had given Denmark the lead, only for VAR to spot a very tight offside.
Soon afterwards on 53 minutes, the same player was adjudged to have handled in the box after a review and Havertz found the corner of the net beyond Kasper Schmeichel's dispairing dive.
Schlotterbeck's superb long pass then released Musiala on 68 minutes and the mercurial playmaker made no mistake. The Bayern Munich youngster is now Euro 2024 joint top scorer with three goals.
Denmark midfielder Thomas Delaney told TV2: "It really hurts right now. We were playing a good team, but we just needed to stick the knife in today."
Germany coach Julian Nagelsmann sprang two surprises by replacing left back Maximilian Mittelstädt with David Raum and Florian Wirtz with winger Leroy Sané.
Centre back Antonio Rüdiger was fit to start in Dortmund, with Schlotterbeck coming in for the suspended Jonathan Tah alongside him.
Meanwhile, Denmark midfielders Christian Eriksen and Thomas Delaney started after overcoming stomach bugs.
Watched on by German Chancellor Olaf Scholz, the hosts made a flying start with Dortmund's Schlotterbeck heading in Toni Kroos' corner on 4 minutes, but English referee Michael Oliver had already blown for a German foul in the box.
Joshua Kimmich and Havertz then tested Schmeichel as the Danes struggled to get up the field due to Germany's high press.
A long ball over the top was one way of trying to attack but Eriksen's shot was deflected wide.
Heavy rain soon began to pour and the game lost urgency. Thunder and lightning then forced the players off.
Even hail began to fall and torrents of water cascaded off the stand roofs. The Dortmund turf took a hammering but held up well when the game restarted.
Germany came out flying with two chances, but the Danes continued to be dangerous, Manuel Neuer saving at the feet of Rasmus Højlund.
Andersen thought he had scored just after half-time when Germany had failed to clear the ball following a free-kick into the area. A long video review took place and it was ruled just offside.
Just moments later, Raum's cross clipped Andersen's hand in an unnatural position and Oliver was called to the review area, where he awarded a penalty.
Havertz did the honours for 1-0 but missed a glorious opportunity for 2-0 soon after, as did Sané.
Denmark - semi-finalists in the last Euros - almost levelled but were then exposed at the back thanks to Schlotterbeck's perfectly weighted, curving ball and Musiala netted with aplomb.
A late Florian Wirtz call for Germany was chalked off for offside.
The last time Germany's men played a major tournament game in Dortmund they lost the 2006 World Cup semi-final to Italy.
They have won a World Cup since but then flopped at the next two editions, as well as losing to England at this stage of the Euros three years ago.
Nagelsmann's men did not play at their very best but did enough to avenge Denmark's win in the final of Euro '92.
