After a slow start, the first real chance of the game yielded the first goal on the quarter-hour mark.
A rather lackadaisical clearance from Kasper Schmeichel in the home goal was seized upon by Stuttgart, and the ball found Bilal El Khannouss via a nice flick from Deniz Undav.
The Celtic stopper compounded his original error as he let the Leicester loanee’s rather tame effort slide past him and into the net.
If that was a slight error, then what Atakan Karazor did for Celtic’s equaliser five minutes later was a complete clanger.
Quite who the Stuttgart captain was trying to pick out with his pass across the edge of his own box is unknown, but the ball was seized upon by Benjamin Nygren, who still had work to do but rounded the onrushing Alexander Nubel and slotted home for a gift of a leveller.
Parity did not last long, though, and before the half-hour mark, El Khannouss struck again.
He did well to readjust to meet Angelo Stiller’s deflected cross, but O’Neill will not be happy with his defence as they left the Moroccan international completely free to nod home his second from six yards.
Outside of the gift from their visitors, the Hoops created very little of note in the first half and conceded plenty, as Ermedin Demirovic hooked Jamie Leweling’s flick-on goalbound but was denied by Schmeichel, while Leweling’s own powerful effort from a narrow angle whistled over the bar.
Celtic started the second half brighter, but Die Schwaben still extended their lead just before the hour mark and, once again, there were question marks around Schmeichel.
It was a low and admittedly hard shot from Leweling that found the net, but it was close enough to the experienced stopper that he perhaps ought to have done better.
Demirovic had the ball in the net for what he thought was a fourth for the visitors after linking up with Undav, but the Bosnian international’s deft chip was ruled out for offside.
Nygren forced a good diving stop from Nübel at the other end as the hosts desperately tried to haul themselves back into the tie, but they struggled throughout to build any sort of momentum.
Tiago Tomas also had Schmeichel at full stretch as Stuttgart looked to add to their lead, and while he couldn’t do it on that occasion, the Portuguese forward clipped one home deep in stoppage time with Celtic Park already largely empty.
A three-goal deficit may well be insurmountable for the Scottish champions, as they are now winless in their last five UEL knockout games.
Flashscore Man of the Match: Bilal El Khannouss (Stuttgart)
