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Filip Kostic (right) scored a late winner for Frankfurt to consign Bayern Munich to their first defeat of the season
Julian Nagelsmann suffered his first defeat as Bayern Munich coach on Sunday as Eintracht Frankfurt snatched a dramatic, smash-and-grab 2-1 away win with a late winner from Filip Kostic.
Kostic drilled a low shot past Manuel Neuer seven minutes from time to hand Frankfurt their first win in Munich for more than two decades and condemn Bayern to their first defeat of the season.
"It always hurts to lose, but this defeat hurts a bit more because it was avoidable," Nagelsmann told DAZN broadcaster.
"We were punished today for not taking our chances."
Bayern recorded 20 shots to Frankfurt's five, but failed to capitalise on a dominant performance as they succumbed to their first league home defeat since 2019.
The slip leaves them level on points with their next opponents Bayer Leverkusen, who beat Arminia Bielefeld 3-0 in Sunday's late game to go second in the table.
Kostic's winner also gave Frankfurt their first league win of the season, lifting the pressure on new coach Oliver Glasner.
"It was the first time I have won in Munich as a coach, and you don't forget your first time," joked a beaming Glasner.
"We've been chasing this win for a while now and have had plenty of chances. The fact that we've got it against Bayern makes it even sweeter," added Frankfurt captain Hinteregger.
Leon Goretzka gave Bayern a deserved lead after a dominant first half-hour, slotting in a low finish after a smart lay-off from Robert Lewandowski.
But the hosts were left reeling a few minutes later, as Martin Hinteregger sent a thundering header past Neuer at a corner to level the scores.
Lewandowski almost restored the lead shortly before the hour-mark, but Frankfurt keeper Kevin Trapp denied the Polish star at point-blank range with a brilliant reflex save.
It was the first of a string of second-half stops from Trapp, whose heroics kept Frankfurt in the game before Kostic's winner sealed Bayern's fate.
Defeat means Bayern now top the table only on goal difference after Leverkusen cruised to a comfortable win over Bielefeld.
The win saw Leverkusen climb to second and draw level on points with Bayern, setting up a mouth-watering top-of-the-table clash when the two teams meet after the international break.
Moussa Diaby opened the scoring in an entertaining first half, before Bielefeld's Patrick Wimmer had a backheeled equaliser ruled out by VAR for offside.
Patrik Schick doubled the visitors' lead just a few minutes later, and headed in a third after the break to put the game beyond reach.
Kerem Demirbay rubbed salt in the wound with a late penalty as Leverkusen celebrated their fifth win of the season.
Elsewhere, Nigerian striker Taiwo Awoniyi netted two goals against his old club as Union Berlin fought from a goal down to beat Mainz 2-1 and continue their fine start to the season.
Awoniyi struck twice in four minutes in the second half to give high-flying Union their first away win of the season and fire them up to seventh in the table.
Union loanee Marcus Ingvartsen also scored against his former team mates to give Mainz the lead just before half-time, but it was former Mainz striker Awoniyi who had the last laugh as Union bounced back after the break.
The Nigerian levelled the scores with a cool finish on the counter-attack 20 minutes from time, and sealed the win with an almost identical goal just a few minutes later.
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