Liverpool took the game to Galatasaray from the first whistle, attempting to quieten the raucous atmosphere at Rams Park.
However, while the hosts had initially been on the back foot, they went ahead after just seven minutes when Victor Osimhen headed a corner back across goal for Mario Lemina to nod past a stranded Giorgi Mamardashvili.
Osimhen then missed a golden chance to double the advantage, with his free header floating agonisingly wide.
As the game settled down, both teams enjoyed reasonable spells of possession, with Mohamed Salah and Hugo Ekitike particularly prominent for Liverpool.
Galatasaray, though, created the best chances; Mamardashvili needed to produce a flying save to thwart Davinson Sanchez, Osimhen skied another chance when unmarked, and some backs-against-the-wall defending from the visitors kept the likes of Noa Lang and Gabriel Sara at bay in an all-action first half.
The end-to-end nature of the game continued up until the interval, yet there were surprisingly no more goals.
Within two minutes of the restart, Alexis Mac Allister was inches away from a Liverpool equaliser as the visitors again flew out of the blocks.
But, while their passing game was far superior to that of the Super Lig side, the Reds were still susceptible to swift counterattacks, and Abdulkerim Bardakci gave Liverpool a timely reminder of the Turkish side’s offensive threat.
Salah, meanwhile, was hooked on the hour after a disappointing individual performance, before Osimhen saw a goal ruled out for offside, with Ibrahima Konate nearly made to pay for an underhit backpass.
Ekitike then missed a one-on-one when Ugurcan Cakir stuck out a leg to divert the ball wide prior to Liverpool having a goal disallowed for a Konate handball.
A frantic last 10 minutes failed to produce any further strikes, meaning Galatasaray held on to claim a potentially crucial triumph.
As a result, they have now lost just two of their last 47 home matches in all competitions (W34, D11), while they are also unbeaten in their last 11 home European Cup/UCL knockout matches (W7, D4).
Liverpool, on the other hand, see a three-game winning away run in all competitions come to an end, but they will still be confident that they can turn the tie around in front of their own supporters next week, given the small nature of the deficit.
Flashscore Man of the Match: Gabriel Sara (Galatasaray)
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