Looking to create their most memorable European night in recent history, Celtic wasted three opportunities to take the lead in a golden three-minute first-half period.
Kuhn was first to threaten the hosts, as the former Bayern reserve team player benefited from excellent play by Jota, but his finish was cleared off the line by Raphael Guerreiro. Seconds later, Kühn flashed a low cross across the goalmouth, but Daizen Maeda could not get his feet in order and failed to get on the end of the cross.
Bayern were rattled, most notably when Dayot Upamecano gave possession away whilst trying to play out from the back, but the visitors squandered a three-on-two situation as Maeda opted to strike the ball early instead of feeding one of his two teammates in support.
Despite being second best and largely lacklustre, the hosts showed moments of quality to almost find the opening goal that would have surely secured their progress to the next round.
In the opening five minutes, Michael Olise stood up a cross to the back post for Serge Gnabry, but Alistair Johnston scrambled across the area to deny the former Arsenal man.
On the stroke of half-time, Harry Kane’s shot from the edge of the area rattled the crossbar to serve as a timely reminder to Brendan Rodgers’ men that even an under-par Bayern side were a constant threat.
Kane would play no further part in the game after being substituted at the break, and despite being light up front, the German side created a great chance just two minutes after the restart, but Kasper Schmeichel raced off his line, making a huge save to deny Leon Goretzka.
For all the talk of Bayern’s limited options up front, it was a catastrophic failure in their defence that led to them falling behind.
Both Joshua Kimmich and Kim Min-Jae fluffed their chance to clear the danger, allowing Kühn to bear down on goal and fire his finish beyond Manuel Neuer, levelling the tie.
After going behind Vincent Kompany’s men rallied, with Schmeichel being forced into several fine saves, most notably to deny Goretzka and Kimmich.
With the game heading towards extra-time, Davies was on hand to scramble home a rebound after Schmeichel’s excellent save from a Goretzka header at the death.
That goal sealed Cletic’s fate, sending them crashing out of the UCL despite a defiant display in Bavaria. As for Bayern, they’ll have to wait to see whether they face fellow Bundesliga side Bayer Leverkusen or Atlético Madrid in Friday’s draw.