Second-half goals from Mohamed Salah and Sadio Mane in the space of five minutes helped the Reds earn a crucial advantage ahead of the second leg at Anfield next month.
Julian Nagelsmann's men, who were underwhelming for most of the game, seemed to get better after Liverpool's brace but ultimately failed to cause much trouble for the visitors.
Without further ado, here are five talking points from the game.
#5 Liverpool back to winning ways
Liverpool have endured a torrid season so far, crashing out of two domestic competitions and failing woefully in their Premier League title defence. They currently occupy 6th place on the league standings, 13 points away from leaders Manchester City.
The Reds knew that they had to put in a big performance to overturn their fortunes and try to save their season. The Merseyside giants patiently waited for chances to come by and converted them with great efficiency when they did.
Liverpool were not at their rampant best on Tuesday, but they diligently did the needful to win.
#4 Shambolic defending cost RB Leipzig
RB Leipzig did not have to deal with much attacking pressure from Liverpool as Jurgen Klopp's men took a more cautious approach towards the game.
However, the German giants were the architects of their own defeat. An uncharacteristic mistake from club captain Marcel Sabitzer gave the Reds the opening goal early in the second half.
The Austrian, under minimal pressure, gave a wayward back pass to Lukas Klostermann, who was yards away from the ball. Mo Salah reacted quickly to gain possession of the loose ball and raced away to give his side the lead.
Five minutes later, Nordi Mukiele attempted an audacious clearance in his own half and completely fumbled it, allowing Sadio Mane to pounce and double the visitors' lead.
There had also been a catalog of misplaced passes from RB Leipzig in the first half, which Liverpool did not take advantage of.
#3 RB Leipzig will miss Dayot Upamecano
Dayot Upamecano has been an integral part of RB Leipzig's backline since his arrival from RB Salzburg in 2017.
His impressive showings have generated interest from top sides in Europe, and the Frenchman has now opted for a summer move to Bayern Munich. The move, which has been confirmed by the two clubs, is said to be worth around €42 million.
Against Liverpool, Upamecano was miles above his fellow defenders. He raced from midfield in pursuit of Sadio Mane after an error from Mukiele sent the Reds winger through on goal. The 22-year-old defender could not keep up with the rapid Mane, but his frustration was visible for all to see.
A player with such ability and hunger for success will definitely be missed at RB Leipzig next season.
#2 RB Leipzig suffer from wasteful finishing
In a game that had its end-to-end moments, RB Leipzig came close to opening the scoring on two different occasions.
Dani Olmo was first presented with a chance via a cross from Angelino less than five minutes into the game. However, his header struck the base of the goal post.
The Spaniard then turned provider early in the second half. He played in Nkunku behind the Liverpool defence only for the Frenchman to squander his effort.
In a competition often decided by fine margins, RB Leipzig's inability to score a crucial goal might come back to bite them in the second leg.
#1 Liverpool keep European dream alive
After a dire run of results in the Premier League, the UEFA Champions League is the only competition that Liverpool could realistically win this season.
Knowing that they needed a good result to strengthen their course, the Reds binned their usual high-tempo style and took a more reserved approach to the game.
Salah missed a good chance to give his side the lead in the first half, but this did not discourage Liverpool as they kept their heads and stuck to the script.
RB Leipzig failed to take their chances during the game, and Liverpool were on hand to punish them for it as they grabbed two crucial away goals.
Jurgen Klopp and his men would be relieved to have secured such a crucial win in a season full of lows.