Leipzig struck twice in the final 15 minutes to condemn Celtic to an early exit from the Champions League as goals from Timo Werner and Emil Forsberg earned the Germans a 2-0 win in Glasgow.
A seventh consecutive home Champions League defeat for the Scottish champions equals the competition record and leaves Celtic rooted to the foot of Group F with just one point from four games.
Leipzig’s first away win in Europe or the Bundesliga since April puts them in the driving seat to reach the last 16.
Marco Rose’s men move above Shakhtar Donetsk into second place in the group after the Ukrainians were denied a shock win by a 96th minute equaliser for Real Madrid in a 1-1 draw in Warsaw.
Celtic trail Shakhtar by four points and need to win when the sides meet in two weeks to have any chance of even salvaging Europa League football in the new year.
It was a familiar story for Celtic as a failure to take their chances came back to haunt Ange Postecoglou’s men.