Mohamed Salah scored the fastest-ever Champions League hat-trick as Liverpool turned it on in the second half to thrash Rangers 7-1.
Rangers took the lead through Scott Arfield but the brilliant Roberto Firmino levelled it up and Liverpool took over after half-time, scoring six unanswered goals - including three in six minutes from substitute Salah - to leave the hosts unable to make it through to the last 16.
Firmino got his second to give Liverpool the lead on 55 minutes before the Brazilian's flick set up Darwin Nunez to net his second goal in as many games. Salah then took over, scoring the first of his three goals on 75 minutes and securing the match ball with two more ruthless finishes against the hapless Rangers defence.
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After a such a bright start, it turned into an embarrassing night for Rangers, who lost both Connor Goldson and Ryan Jack to injuries and conceded a seventh to Harvey Elliott that was eventually awarded by VAR.
Liverpool's spectacular second half meant it was Rangers' heaviest-ever defeat in a competitive match at Ibrox. The result left Gers boss Giovanni van Bronckhorst scratching his head.
He said: "The first hour we were there and we can make it difficult for many opponents at Ibrox but the way we played the last 25 minutes, you will lose against any team we play here.
"I cannot explain. I have to process this, I cannot explain at the moment.
"Of course we need to accept the criticism. It's part of my job, part of the players' job.
"When you perform like this - I don't mean the whole 90 minutes, but the last 25 minutes - you will get criticism and we have to take it on the chin."
After Napoli beat Ajax 4-2 earlier in the night, Liverpool now just need one point from their final two games away to Ajax and home to Napoli to assure their qualification. Rangers are bottom after four straight defeats and cannot qualify for the knockouts.
This was a timely boost for Jurgen Klopp's men, who face Manchester City on Sunday, live on Sky Sports.
How Reds ran riot in sensational second half…
Klopp was in a prickly mood in the pre-match press conference, hitting back at Dietmar Hamann's claim that his side "lack spark" but Hamann's view looked vindicated in the opening exchanges as Liverpool yet again conceded the first goal in a match. It has now happened in eight of their last 13 games across all competitions.
Arfield was the man to send Ibrox delirious, finishing off a flowing move courtesy of a defence-splitting Jack pass. It was Rangers' first goal of the group stage.
Klopp's men looked lost as they tried to stage a fightback as Joe Gomez played an inexplicable blind pass back to Alisson and Antonio Colak should have done better with his finish.
Despite all Liverpool's problems, the form of Firmino continues to shine.
He notched at a key time with Liverpool struggling when flicking home a Kostas Tsimikas corner to draw his team level.
The goal was to be Liverpool's last shot of the half as Rangers played the more creative football. Arfield squandered a fantastic chance from 10 yards after some rapid wing-play from Fashion Sakala.
The home fans would have been confident of witnessing a famous European night at Ibrox but a different Liverpool appeared after the break, playing with their usual level of zip and intensity.
Nunez - who played yet again like a man trying too hard - curled a wayward effort when squeezing in behind the Rangers back four. Firmino showed him how it should be done on 55 minutes.
Gomez played the Trent Alexander-Arnold role down the right by scorching into space and delivering the perfect final ball across goal that was finished in confident fashion by the flying Firmino.
Liverpool were now playing at a level Rangers had no answers for as Firmino played a no-look flick into the path of Nunez, who swept a finish into the bottom corner.
That was Nunez's last act as Salah replaced him on 68 minutes. Not a bad substitute to have in reserve.
His first goal was a classic Salah finish, killing the ball out of the sky down the right and poking a fantastic finish despite a nearly impossible angle.
Thiago, Firmino and Diogo Jota played their part in his second goal as some lovely build-up ended with Salah squeezing another lovely strike past Allan McGregor. The cameo of all cameos was complete a minute later when Salah collected another Jota pass and curled one into the far corner.
As easy as one, two, three.
That was not the end of the torture for Rangers, whose defensive line was all over the shop as Elliott smacked home his first Champions League goal after VAR had reversed a wrongly-flagged offside on Jota.
By this point, Liverpool were playing a different sport to Rangers. A chastening evening for the hosts.
Klopp: The mood has changed
Jurgen Klopp said: "It changed the mood definitely. It's completely different. We usually drink a beer after away games but it's that long ago I drunk a beer I'll probably be drunk after one. Yes, it changed the mood completely but we all know who we are welcoming on Sunday and this will be a different game but it's better to go into it with this feeling we've got tonight than any other.
"All the goals were great, how we set them up and finished them off.
"Typical Mo [Salah]. Very important, the whole thing, how the boys adapted to it, to the positions, to the line-up, the reaction of the boys on the pitch, I thought everybody who started tonight played really well, I can't think of one player who didn't have a good game, the two kids right and left wing really good, Fabio [Carvalho] and Harvey [Elliott], and when you can change like we did tonight and the boys come on ready to contribute then things like this can happen.
"A freak result, we all know that, and we don't make more of it than we should, but obviously it's the best we could have asked for and I'm pretty pleased."
GVB: We conceded too many easy goals
Rangers manager Giovanni van Bronckhorst speaking to BT Sport: "It was a very disappointing result. We played well first half and were in the game.
"The second goal - we know their strength. When you lose the ball in the middle of the pitch they are so fast on transition. We got caught a couple of times.
"We conceded too many easy goals. It went pretty quickly after that. We tried to push, but after the 3-1 you could see we were struggling. They upped the tempo and we weren't accurate in our passing."
Opta: Super Mo
- Salah has scored 38 UEFA Champions League goals for Liverpool, now the most by any player for an English club in the competition, surpassing Didier Drogba for Chelsea and Sergio Aguero for Man City (both 36).
- With just six minutes and 12 seconds between his first and third goals, Liverpool's Salah scored the fastest-ever UEFA Champions League hat-trick.
- Liverpool have won nine of their 10 UEFA Champions League group stage games since the start of last season (L1), including each of their last three.
- Rangers conceded seven goals in a single match in European competition for a very first time.
- Only Erling Haaland (23) has more goal involvements for Premier League clubs in all competitions this season than Firmino (12 - 8 goals, 4 assists).
What's next?
Rangers return to Scottish Premiership action on Sunday as they go to Motherwell, live on Sky Sports Football from 11am; kick-off 12pm.
Van Bronckhorst's side then face Dundee at home in a Scottish League Cup quarter-final on October 19 at 8.15pm.
Then three days later, the Gers host Livingston at Ibrox in the Scottish Premiership in a 3pm kick-off.
Liverpool's next game is on Sunday as they host champions Manchester City, live on Sky Sports.
The Reds have another home game three days later on October 19 as they welcome West Ham to Anfield in a 7.30pm kick-off.
Then Jurgen Klopp's side face Nottingham Forest away on October 22 in a 12.30pm kick-off.