For Rudi Völler, the unlikeliest of hat-tricks came after the final whistle. "I will celebrate a win with Kölsch, Pils and Weissbier," the Bayer Leverkusen sporting director had threatened in the Bayern Munich stadium magazine beforehand, mainly in jest. Everyone knew that Leverkusen could not possibly win in the Allianz Arena on Sunday night. Leverkusen not winning in Munich is one of the axiomatic laws of the Bundesliga, a bit like Thomas Schaaf wearing a moustache (or the other way round), Schalke not winning the league and Uli Hoeness buying players who score against Bayern.

Völler, naturally, couldn't quite believe what he witnessed. "It will be a tough night for me," the 52-year-old joked when the "madness" – Stefan Kiessling's verdict – had become reality. Leverkusen greeted the 2-1 win, their first in the capital of Bavaria since Marek Lesniak downed Bayern with a solitary goal in the Olympic stadium in October 1989, with the incredulity of a whole-life tariff prisoner who has just received a real "get out of jail free" card in the post. "Now our time of suffering is over and we have been freed from the jinx," Kiessling, the scorer of the first goal, exclaimed.

"The curse has been expunged from the history books," Kölner Stadt-Anzeiger wrote, getting their football cliches all mixed up in the excitement. It certainly was not a normal win. The Leverkusen players could be heard dancing and singing to loud music in the changing room long after what Express called the "sensation".

It was not just Leverkusen's well-deserved reputation as bottlers in Munich – "when we go there, it always smell of shit, we really have our nappies full," their former general manager Reiner Callmund once quipped – that made the result so surprising. Bayern had also come into the game with an unblemished, historic record of eight league wins in a row while the immensely talented if maddeningly inconsistent visitors had lost to Eintracht Frankfurt and Borussia Dortmund and played out disappointing draws with Stuttgart and Mainz.

Their coaches Sascha Lewandowski and Sami Hyypia adopted a flexible strategy with some sporadic high-pressing and a 4-3-3 system that mostly saw all of their players behind the ball. The hosts huffed and puffed without ever creating a convincing opening, Leverkusen were happy to threaten on the counter. On one such rare occasion, André Schürrle underhit a low cross but Philipp Lahm inexplicably helped the ball on to Kiessling's foot. That made it 1-0, shortly before the break. It was only the third goal Bayern had conceded in the whole domestic season.

Bayern were intent on treating the deficit as a mere inconvenience after the break. Jupp Heynckes moved David Alaba back to left-back in place of the injured Holger Badstuber and threw on Xherdan Shaqiri. Again, they threw plenty of bodies forward, but Leverkusen, led by the stealth of their captain Simon Rolfes and the superb centre-back Philipp Wollscheid, stood firm. In addition, the Reds' cause was not helped by their attacking fulcrum Toni Kroos getting lost in a sea of white shirts and some of the most futile, hopeless crossing seen since level 15 of Frogger.

The Bayern substitute Claudio Pizarro found the breakthrough with his first telling intervention of the season, playing in Mario Mandzukic for the equaliser with 13 minutes remaining but Leverkusen refused to let the match be shaped by the usual narrative. A lack of nerve and the ultra-defensive – or cowardly – tactics of the second half, when Kiessling was often the furthest man forward 30m inside his own pitch, would obviously have been blamed for the reversal. But they came forward once more to discover another German football axiom: where there's a Boateng, there's a way.

Jérôme Boateng was having one of his regular mini-naps to allow Sidney Sam run in behind him, then rather comically diverted Sam's corner-flag-bound header into the net by getting hit in the face after 86 minutes. "We scored the goals against us ourselves," Manuel Neuer said. Neuer nearly set up a last-minute equaliser for Pizarro at the death with a fine dribble near Leverkusen's box, but the Pervuian only clipped the bar with his header.

"I'm happy that the team were able to get such a big result," Lewandowski said. Lifting the Munich curse is perhaps less important for this campaign than the main lesson of this utterly convincing performance: they have found a system that brings out the best of the squad. Playing with three central midfielders gives the tucked-in wingers Schürrle and Gonzalo Castro the freedom to support Kiessling, a striker who does not quite have the required presence on his own. Leverkusen's excellent counterattacking could prove every bit as successful as Gladbach's did last season. They will now believe that fourth place and Champions League football, their aim for the season, is well within their reach.

Bayern, on the other hand, woke up to headlines that questioned their mettle. "Will anxiety set in now?" Bild wondered. A slight overreaction perhaps, but they do have previous in this regard. Last season, a bad autumn saw them relinquish an eight-point lead after they had started with seven wins. "We're comfortably ahead of our competitors and won't be fazed by this defeat," Heynckes said in an effort to downplay the result. Karl-Heinz Rummenigge sounded a bit more ominous, however. "There will be pressure on the team now," the CEO said. "I'm curious to see how they'll deal with it." The two supposedly crucial changes of this season – a much bigger, better bench and a bigger winning mentality, courtesy of the relentlessly ambitious sporting director Matthias Sammer – will be put to the test in the away trip to Hamburg next week.

Talking points

• Felix Magath was fired on Thursday afternoon. The Wolfsburg players denied that there had been a popular revolt and secret ballot – surely polling the 60-odd players in the squad would have been very impractical – but there was more than a whiff of "Lower Saxony Spring" in the air on Saturday. Freed from the shackles of Magath's despotic and increasingly erratic regime, the Wolves stormed to a 4-1 away win at Düsseldorf under their caretaker manager Lorenz-Güntner Köstner, who had been informed of his appointment on the way out of a sauna by a call from a tabloid hack.

"The confidence was back, no one was afraid to make mistakes," Diego said. "I hope that the old manager will get happy. We are now."

• While Dortmund played out a slightly fortunate 2-0 win on Freiburg's snowy pitch – "Mama used to forbid us to play in these conditions, now we have to," Jürgen Klopp joked – Schalke ended their perfect week with a patient 1-0 over Nürnberg. The Royal Blues are only four points behind Bayern now. "This was a dirty, laborious win," their captain Benedikt Höwedes said.

• Frankfurt's Alex Meier scored a gorgeous goal and inadvertently knocked out one of Georg Niedermeier's teeth after a clash of heads but it was not quite enough to floor the Swabians. Bruno Labbadia's men registered an extremely fortunate 2-1 win in the Mercedes-Benz-Arena that will ease the pressure on the coach – at least for another week. Frankfurt were also robbed at the end; a Karim Matmour goal was wrongly ruled offside. "It's not the end of the world," the Eintracht manager Armin Veh said with characteristic serenity.

• Elsewhere poor Tim Wiese came back to star, if that's the right word, as a human dart-board again: the Hoffenheim keeper conceded his 19th, 20th and 21st goal in his fifth game of the season. The Mainz striker Adam Szalai scored a hat-trick, the Hoffe coach Markus Babbel went on his tried and tested "the players don't want it enough" trip, and someone in Spain is still having laugh. According to El Mundo Deportivo, Real Madrid are following Wiese's (lack of) progress with a view to a possible transfer in the summer. It sort of makes sense: El Mundo are of course a Barcelona-supporting paper.

Results: Augsburg 0-2 Hamburg, Bayern Munich 1-2 Bayer Leverkusen, Düsseldorf 1-4 Wolfsburg, Greuther Fürth 1-1 Werder Bremen, Schalke 04 1-0 Nürnberg, Freiburg 0-2 Borussia Dortmund, Stuttgart 2-1 Frankfurt Hannover 2-3 Borussia Mönchengladbach.

• Find out the latest Bundesliga standings here