On an evening where both goalkeepers wore their best gloves but neither set of attackers found their best shooting boots, Darwin Nunez's first-half toe-poke was the telling moment, but Arne Slot's side had to survive a scare or two to make it nine points from nine.
The midweek meeting was a clash of perfect and pointless, as the Reds were two for two while their hosts did not boast a single point from their opening couple of matches, but Marco Rose's side showed plenty of attacking intent early on.
However, neither Leipzig nor Liverpool were proving adept at keeping hold of the ball - both seeing attacks break down due to sloppy passes - but the German outfit were denied a wonderful opener by Lois Openda due to the offside flag.
Just a couple of minutes later, Liverpool went down the other end and broke the deadlock when Nunez made sure Mohamed Salah's header crossed the line, although the Uruguayan was then inexplicably denied a seemingly stonewall penalty on the stroke of half time.
Nunez was not the only anguished attacker at the Red Bull Arena, though; Leipzig's front three were being repeatedly repelled in the second half by an inspired Caoimhin Kelleher, who spared the blushes of his somewhat lethargic teammates on several occasions.
While Kelleher's luck of the Irish was in, Openda's was not, as the Belgian had another goal disallowed for offside in the final 10 before he bizarrely tried to square for Yussuf Poulsen when the shot was on - he had failed to time his run as well on that occasion, though.
One of only two sides to win their opening three games of the 2024-25 Champions League, Liverpool sit second in the 36-team league table - only behind PL rivals Aston Villa on goal difference - while Leipzig are 31st but are the highest of all the zero-point clubs.
LEIPZIG VS. LIVERPOOL HIGHLIGHTS
Darwin Nunez goal vs. Leipzig (28th min, Leipzig 0-1 Liverpool)
After Openda's wonder strike was disallowed, Nunez steals in to steal a goal from Salah!
Cody Gakpo and Kostas Tsimikas combine well down the left, and the latter sends a cross to the back post for Salah, whose header is bound for the bottom corner as Peter Gulacsi and the Leipzig defence wait for the inevitable.
The stagnant Willi Orban fails to notice Nunez charging in behind him, though, and the South American toe-pokes the ball over the line just to make sure - a penny for Salah's thoughts though!
Darwin Nunez denied penalty vs. Leipzig (38th min, Leipzig 0-1 Liverpool)
Nunez and Orban are in the spotlight once again, and the latter should have breathed the biggest sigh of relief in his life after somehow escaping giving away a spot kick.
The effervescent Nunez just about manages to get to Gakpo's through ball before the Hungary centre-back and goes down under his challenge, but both the on-field referee and VAR agree that no action is warranted.
Replays show that Orban clearly made contact with Nunez's lower leg, but the ball was sailing behind for a goal kick anyway, which may have saved Orban's bacon.
MAN OF THE MATCH - CAOIMHIN KELLEHER
It has been said many times before that Kelleher is the best number two in the Premier League, and the Republic of Ireland international once again justified such a description on Wednesday, where he made a multitude of fabulous stops to keep the hosts at bay.
Kelleher made a total of six saves at the Red Bull Arena, and a 2025 transfer to a club where he will be an undisputed number one surely beckons.
A word for Kelleher's opposite number Gulacsi too, as the former Liverpool goalkeeper also did his bit to keep the scoreline respectable with a string of top saves.
LEIPZIG VS. LIVERPOOL MATCH STATS
Possession: Leipzig 42%-58% Liverpool
Shots: Leipzig 13-17 Liverpool
Shots on target: Leipzig 6-8 Liverpool
Corners: Leipzig 5-7 Liverpool
Fouls: Leipzig 9-7 Liverpool
BEST STAT
WHAT NEXT?
In terms of Champions League action, Liverpool's fourth match of the 2024-25 tournament is a mouthwatering one - at home to Xabi Alonso's Bayer Leverkusen on November 5 - while Leipzig travel to Celtic on the same evening.
In the more immediate future, Slot's men head to Arsenal for Sunday's Premier League main event, one day after Die Roten Bullen host Freiburg in the Bundesliga.