The Mexican waves were going around the Stade Pierre Mauroy well before this game was over, a measure of the ease with which Germany turned this tricky fixture into a sort of Teutonic village fete. At one point you almost expected Toni Kroos to request a stein of beer and swig from it while he ran the game. This was Germany’s best performance of the tournament by some distance, perhaps even the best by anyone, and it establishes them, along with France, as the clear favourites to win.

All bets were off from the moment Jerome Boateng gave them an early lead with a spectacular volley from 25 yards, scuppering Slovakia’s game-plan which had not been working that well anyway. After which, Germany’s magnificent defence simply took over. Their pressing was exemplary, and, with Slovakia forced to come forward, Germany could simply bide their time and pick them off. Mario Gomez and Julian Draxler completed the victory with goals either side of half-time.

One way or the other, revenge will be next on the menu for Germany. They will meet either Italy or Spain in Saturday’s quarter-final in Bordeaux, the countries who have eliminated them from each of the last two tournaments. “They will demand much more from us,” said Gomez. “The Spanish will attack while the Italians will play defensively. We just have to play our game, and then we can proceed.”

Draxler, who replaced Mario Gotze in the starting XI, was worthy of special mention. It was a close-run thing between him and Boateng, but he was probably the best player on the pitch, having offered up a masterclass in modern wing play. As well as being the first line of defence, he was a constant outlet for the midfield, squirmed out of trouble time and again, got his cross in time and again.

Gomez scored for the second consecutive game and although there are still kinks to iron out, there is a sense that this Germany team are beginning to purr at the just the right moment. Slovakia, who had beaten Germany 3-1 in a friendly only last month, could not get close to containing their speed of thought and intelligence of movement. It also put the Slovaks rearguard against England last Monday into a certain perspective.

Marek Hamsik, so good earlier in this tournament, was disappointing here. He misplaced too many passes, did not play enough telling ones and generally failed to exert the influence required if Slovakia were to get close to an upset.

The 3-0 defeat might even have been worse. In the 13th minute Martin Skrtel tried to push and pull Gomez like a locked door, whereupon the Polish referee awarded a penalty. Up stepped Mesut Ozil with a languid, two-yard approach, as if he was about to bowl an over of left-arm spin, and put the kick at a comfortable height for Matus Kozacik to save.

That was probably about as good as it got for Slovakia. Gomez tapped in at the near post after lovely work by Draxler down the left, and then on the hour Draxler got the goal he deserved, smashing in a volley from close range.

“It has been a beautiful tournament,” said the gracious Slovakia coach, Jan Kozak.

“The German team were in full swing, and difficult to neutralise. I will be leaving this tournament with nothing but nice memories.”

Do Germany have any genuine weaknesses? It is a question that Spain or Italy will be able to answer with more conviction. Perhaps Mats Hummels is still half a yard short of full sharpness after a recent injury. Perhaps better defences will be able to nullify Gomez more easily. But there was something unambiguous in Germany’s manner – call it swagger or poise – that suggested they were not harbouring any of those doubts themselves. That is what will worry everyone else.