Two second-half goals from Mohamed Salah and Sadio Mane secured Liverpool's place in the last eight of the Champions League.
It was déjà vu from the first leg, just over a month ago as the two dangermen piled on the misery for RB Leipzig.
An incisive break from the Reds saw the front three of Mane, Diogo Jota and Salah combine, the Egyptian cut inside and slotted the ball in the bottom corner.
Minutes later it was two, Divock Origi made the goal with great hold up, before moving out wide, he picked out Mane at the back post who poked home.
The road to number seven continues as the Premier League champions march on to the last eight.
Liverpool dominate but rue missed chances
Similar to the first leg, Dani Olmo had the first big chance of the match. The Liverpool defence Christopher Nkunku splitting through ball caused problems, Andy Robertson recovered well but the loose ball trickled to the Spaniard only to be denied by brilliant reflexes from Alisson.
Diogo Jota had the first chance for the 'hosts', Lukas Klosterman misjudged the flight of the corner but the Portuguese forward goalwards header forced Peter Gulacsi into a reflex save.
Liverpool came close after an incisive break from Thiago's bicycle kick set Mohamed Salah through on goal, he fired at Gulacsi, Sadio Mane was steaming forward but missed his header, before the Senegal international was penalised for a high boot.
Emil Forsberg had a flurry of chances, his first effort was a curling effort but easy for Alisson.
Then Leipzig caught Liverpool out of position, Nkunku found Forsberg, the Swede tried to slip the runner through before a deflection gave him a clear sight of goal but his drilled effort fizzed past the wrong side of the post.
Jota, fortunately, found space in the middle of the pitch, his effort stung the palms of Gulacsi.
Liverpool wasted a golden chance in the final minute of added time, Salah brilliantly controlled a long-searching pass but Dayot Upamecano made a crucial interception but the loose ball left the goal gaping, only for Jota to fire into the side-netting.
Liverpool pressed well.
Scared to shoot in the key moments.
Looked a completely different team from Sunday, pressing, interplay and movement all good.
Look susceptible to counter-attack at times with the high line not helping that.
Should've taken our chances first half.
Ste's first half thoughts: Liverpool were unlucky not to be ahead at the break having squandered a number of guilt-edged chances with Diogo Jota having the majority of them.
The midfield trio everyone has been waiting for was a joy to watch, Thiago brilliantly composing attacks, Fabinho halting any real threat. Alisson called into action early but made a brilliant save.
Deja-vu in Budapest as Salah and Mane fire Liverpool through
The second half was tightly contested. Liverpool lacking quality in the final third, Julian Nagelsmann added firepower to Leipzig's front line.
Hwang Hee-Chan fired over with his speculative effort.
Second-half substitute Alexander Sorloth lifted his header and had Alisson beaten all ends up only to be denied by the crossbar.
The warning signs were there for Liverpool.
But with 20 minutes left, the front three combined, Mane to Jota, wide to Salah, the Egyptian king cut inside and found the bottom corner.
Moments later, their place in the last eight if it was in any doubt, was confirmed.
Another well-worked Reds passage of play, substitute Divock Origi found Mane at the back post who poked home.
Origi was searching to get on the scoresheet himself, he found space on the far side, he came inside onto his favoured right foot but couldn't only fire into the side-netting.
The goal scorer for Liverpool's opener was hungry for more, he had the Leipzig defence on the back foot, he cut inside as he did for the first goal but his effort deflected wide.
71: Great goal from Liverpool, quick break, great pass from Mane, good vision from Jota and topped off with a cool finish from Salah.
Couldn't keep the ball in the opening stages, intricate passes were just one too many, at times.
55: Can't finish - may of been offside - but can't find the back of the net.
Lacked quality on the last pass in the final third.
65: Leipzig looked very dangerous - Sorloth hitting the bar was a real warning sign.
Ste's second half thoughts: A slow second half but a brilliant display from the Reds. What a sight to see Nat Phillips winning everything in the air, the front three combining for the opener and Mane back on the scoresheet.
LFC Transfer Room Verdict
Priyasha said: "A classy 90 minutes worth of performance from Liverpool after a long, long, time.
"The midfield, the defence as well, had absolute masterclasses, only the attack was not on point.
"Thiago with Fabinho in the middle was more than just a delight to witness and Nathaniel Phillips was a monster in the back, rising to yet another occasion when we needed him.
"The only concern from the match is how our forwards seemed to have lost their shooting boots."
A delighted Ritchie said: "Absolutely fantastic win and performance. Liverpool have had so many great European nights and this is an important one to hopefully get our momentum back.
"Fabinho made a huge difference to how we win regain possession. The Brazilian gave the entire team complete confidence to play their natural way.
"We saw Thiago unleashed, the Centre-Backs looks more assured with him in the 6 and both fullbacks could attack.
"Into the last eight; this season isn’t over yet!"
Once again not a trademark Liverpool performance by any stretch of the imagination.
Chances have to be put away in the future, but like the first leg a professional job.
The defence was resolute, the midfield trio we were all waiting for played magnificently and in the end, the front three came together and rounded off a brilliant attacking goal.
Wolves on Monday is another big game in the aspect of the league, but the season remains relevant with advancing into the next stage.
Get through unscathed to the international break, get the long-awaited break they've been waiting for then when we come back against Arsenal, who knows who'll be back but this is a good sign and a very bright start.
More minutes in the bag, finally back amongst the goals 'at home' and more importantly in the hat for the next rounds in 11 days time, can't ask for much more.
The quest for number seven at the Ataturk in Istanbul continues.
Liverpool: Alisson, Alexander-Arnold, Phillips, Kabak, Robertson, Fabinho, Wijnaldum, Thiago, Mane, Salah, Jota.
RB Leipzig: Gulacsi, Adams, Mukiele, Upamecano, Klostermann, Nkunku, Olmo, Kampl, Sabitzer, Forsberg, Poulsen.
Goals: 71' Salah, 74' Mane.
Subs: 71' Keita & Origi (on for Thiago and Jota), 82' Milner (on for Wijnaldum), 89' Tsmikas & Oxlade-Chamberlain (on for Robertson & Mane); 45' Sorloth (on for Kampl), 61' Kluivert & Hwang (on for Forsberg & Poulsen), 73' Haidara (on for Olmo)