Kasper Schmeichel made a couple of costly errors as Stuttgart put one foot in the Europa League round of 16 with a 4-1 away win over Celtic.
Martin O'Neill's side only survived the league phase due to a rousing 4-2 victory over Utrecht on matchday eight, but their European campaign is now hanging by a thread after an error-strewn showing in the first leg of their play-off tie.
A poor clearance from Schmeichel led to Celtic falling behind in the 15th minute, though Stuttgart still had plenty to do after seizing possession, with Deniz Undav's glorious backheel volley picking out Bilal El Khannouss, who drilled home left-footed.
Celtic equalised six minutes later thanks to a mistake at the other end, as Atakan Karazor attempted a blind pass while facing his own goal, which deflected kindly for Benjamin Nygren to round Alexander Nubel to tap in.
However, another El Khannouss goal restored Stuttgart's lead in the 28th minute, as he nodded a deflected cross in at the near post.
Things got worse for the hosts 12 minutes into the second half, with Jamie Leweling's dipping effort from distance bouncing through Schmeichel's grip and into the net, causing the Dane to be booed by his own supporters.
Stuttgart saw a potential fourth goal chalked off after Ermedin Demirovic was ruled offside, but they will go into their home leg with a three-goal advantage after substitute Tiago Tomas flicked over Schmeichel in stoppage time.
Data Debrief: Stuttgart fill their boots in dominant win
This fixture held fond memories for O'Neill, who led Celtic to a 5-4 aggregate success over Stuttgart en route to a runner-up finish in the 2002-03 UEFA Cup.
But his team were powerless to resist as Stuttgart ran riot in Glasgow. El Khannouss, at the age of 21 years and 285 days, became the youngest player to score multiple goals in a European fixture for Die Schwaben since Mario Gomez against Rapid Bucuresti in the 2005 UEFA Cup (20 years, 157 days).
Undav, meanwhile, became only the sixth player from Europe's top five leagues to reach double figures for goals (16) and assists (11) this season (all competitions), after Michael Olise, Luis Diaz, Lamine Yamal, Fermin Lopez and Marcus Rashford.
Leweling's four goals from outside the area in all competitions this term are now the most by any Bundesliga player, though his strike, in truth, should have been stopped by Schmeichel.
The Dane's poor performance contributed to Stuttgart scoring four goals from 2.08 xG, while Celtic underperformed their 1.79 xG, with Julian Araujo somehow turning wide on the stretch in the Bhoys' last action of the game.