Kostic picked up the ball on the edge of the box, charged forward and beat goalkeeper Manuel Neuer with a powerful low drive to seal Eintracht’s first win of the season and snap Bayern’s nine-game winning run in all competitions.

The Bavarians had only themselves to blame for not killing off the game earlier with a string of golden chances but remain top of the table with 16 points from seven games, one ahead of Borussia Dortmund and Freiburg in second and third respectively.

“We are obviously disappointed, frustrated and angry,” said Bayern midfielder Thomas Mueller. “It was a game that we should never have lost but we were not efficient enough.”

Eintracht, whose last league victory in Munich was in 2000 before the Allianz Arena was even built, are on eight points in 13th place.

The home side took the lead when Leon Goretzka benefited from a Martin Hinteregger mistake to score in the 29th minute.

The Austrian defender, part of a five-man Frankfurt defence, quickly made amends by powering a header into the net for the equaliser three minutes later.

Both teams each had a chance to take the lead before the break with Eintracht’s Almamy Toure forcing a superb save from Neuer in the 43rd minute and Bayern’s Serge Gnabry hitting the post from close range a minute later.

Eintracht keeper Kevin Trapp was kept busy in the second half, repeatedly denying Gnabry, Leroy Sane and Robert Lewandowski as the hosts pushed forward in search of the winner.

Bayern were punished for their missed opportunities though when Eintracht scored what proved to be the winner against the run of play through Kostic before Trapp made another key save in stoppage time to palm a Goretzka shot wide.