Timo Werner and Emil Forsberg netted in the final 15 minutes as they ended Celtic's hopes of Champions League progression.
It was a similar pattern for Ange Postecoglou's side who missed a host of big first half chances, before eventually being punishedafter a lack of clinical finishing. The back to back wins for the Bundesliga side coupled up with Shakhtar's draw with Real Madrid leaves the Hoops cut adrift at the bottom of the section with just one point from four games.
The result means any hopes of progression from the group to the last 16 stage are over with even a place in the Europa League by finishing third a real uphill task for the Scottish champions. Here's three things we learned from Celtic's defeat to Leipzig.
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Make it count
Celtic one again had numerous big chances that they failed to take.
At the very top level you have to take these opportunities when they come.
Daizen Maeda missed an early header while Matt O'Riley smashed the base of the post with Greg Taylor's follow up hitting the bar.
Kyogo Furuhashi then headed over when he really should have tested the keeper at minimum from Sead Hakšabanovićs cross.
Maeda was guilty of another miss from a decent chance as he volleyed wide from an Aaron Mooy cut back.
Once again they were punished as Timo Werner headed home before Emil Forsberg netted a second.
Growing injury concerns
Liel Abada was the latest Celtic star to limp off injured.
The Israeli international looked to suffer a knock to his knee just before half-time and was replaced by James Forrest.
Callum McGregor suffered an injury in Germany against the same opposition last week while Jota missed out tonight.
Cameron Carter-Vickers and Giorgos Giakoumakis are just off the injury table with Carl Starfelt remaining out.
It's a run of bad luck that will be concerning Postecoglou.
Eur out
Celtic' Champions League campaign is officially over on matchday four.
The Hoops have picked up just one draw from four outings in the section and are now cut adrift in fourth position.
RB Leipzig - who completed the double over Ange Postecoglou's side - are five points clear in second spot with hopes of even reaching the Europa League looking a very tall order with Shakhtar sitting four ahead in third.
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