Mohamed Salah scored in the 75th, 80th and 81st minutes to record a stunning hat trickMohamed Salah came off the bench to score an incredible six-minute hat-trick as Liverpool obliterated Rangers in the Champions League.
The striker netted three times in his sensational first 13 minutes on the pitch to silence a once-euphoric Ibrox crowd.
Scott Arfield had given Rangers an early lead with their first group goal, but a Roberto Firmino double and a Darwin Nunez strike set Liverpool on their way, with Harvey Elliott getting a seventh after a VAR check.
It was a mesmeric second-half performance from the Premier League club, who now just need a draw against Ajax in Amsterdam in two weeks to advance to the next stage.
A beleaguered Rangers are still searching for their first points, and their hopes turn to trying to finish third in Group A and claim a Europa League place. It does not get any easier for them, though, as they travel to face group leaders Napoli next.
As Salah trotted on to the Ibrox pitch, it was with little fanfare. Nunez had just given the visitors a commanding 3-1 lead, and the Egyptian's introduction seemed almost like the cherry on the cake after a tasty game had been yanked away from Rangers.
But a player whose stellar form has dipped to merely good this term produced something special.
It started with an old-fashioned toe poke from a tight angle. Salah was off and running. A handful of minutes later, a drop of the shoulder, a quick change of pace on the edge of the box, and a deceptive finish brought his second. Ibrox, not for the first or last time in the half, fell silent.
There was barely time to type his name as the player of the match before his astonishing intervention was complete with yet another composed finish.
After just 17 minutes of this frenzied contest, it looked all so different. All of Liverpool's wins since August have come in Europe, but another looked unlikely amid a cacophony of noise in Govan.
A flowing Rangers move cleaved open a static Liverpool defence and allowed Arfield space to steer a shot low across Alisson and into the net. Finally Rangers had arrived in this year's Champions League.
It was an arrival which was celebrated for seven minutes. Kostas Tsimikas' whipped corner to the near post found an unmarked and grateful Firmino, who nodded in from six yards.
Ten minutes after the break, Firmino hushed a raucous crowd again. Joe Gomez's rampaging run down the right created the opening, and his inch-perfect delivery found the Brazilian on the run for a low first-time steer through Allan McGregor's legs.
The writing was on the wall for Rangers by this point, and it was absolutely game over on 66 minutes. Again Firmino was involved, his cute flick teeing up Nunez for a curling shot around McGregor from the edge of the box for a goal met with a ferocious punch of the air by manager Jurgen Klopp.
After Salah was finished stealing the show, there was still time for more as Elliott got in on the act. The youngster was originally flagged for offside after volleying in, before a VAR check reversed the decision and sent him jogging away in celebration to a jubilant band of supporters in the far corner.
Player of the match - Mohamed Salah
I mean, do we need an explanation? An incredible late cameo that turned an impressive win into a rout in six minutesLiverpool rouse themselves to send message - analysis
This was a result Liverpool needed, but the scoreline will send a warning that they are still capable of being imperious.
Apart from Firmino's opener, they did not look clinical in front of goal in the first half. They were also playing themselves into trouble at the other end.
But the Brazilian played a starring role in turning the tide. His link-up play was a joy to watch, while his finishing and influence was key as Liverpool ran riot after the break. Then enter Salah...
Rangers, meanwhile, now sit bottom of Group A with a goal difference of minus 15 and zero points. The heat of Seville and the Europa League final has long since faded as a winter of discontent on the continent brews.
There is still time for Giovanni van Bronckhorst's team to secure some sort of European football after Christmas, but there won't be too many inside Ibrox for this one who will have much hope of them doing so.
Match stats
Liverpool have won nine of their 10 Champions League group stage games since the start of last season (L1), including each of their last three.It is the second time Rangers have lost their first four games of a Champions League campaign, after doing so in 1996-97. They are the only Scottish side to have done so.Rangers conceded seven goals in a single match in European competition for a first time.With just six minutes and 12 seconds between his first and third goals, Salah scored the fastest ever Champions League hat-trick.Aged 33 years and 345 days, Arfield was Rangers' third-oldest Champions League scorer, after Ally McCoist (34y 57d) and Richard Gough (34y 243d). His opener was Rangers' first goal in the competition since Kenny Miller's against Bursaspor in December 2010, 11 years and 309 days ago.No player has assisted more Champions League goals for Liverpool than Firmino (12, level with Steven Gerrard and James Milner).Salah has scored 38 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).What next?
Liverpool go to Amsterdam on Wednesday, 26 October (20:00 BST) needing a draw against Ajax to progress. Rangers travel to Italy to take on Napoli at the same time.
Player of the match
Mohamed SalahMohamed Salah
Rangers
Squad number37Player nameArfield
Squad number1Player nameMcGregor
Squad number6Player nameGoldson
Squad number26Player nameDavies
Squad number30Player nameSakala
Squad number8Player nameJack
Squad number14Player nameKent
Squad number2Player nameTavernier
Squad number4Player nameLundstram
Squad number10Player nameDavis
Squad number9Player nameColak
Squad number38Player nameKing
Squad number31Player nameBarisic
Squad number17Player nameMatondo
Squad number23Player nameWright
Squad number20Player nameMorelos
Line-ups
Rangers
Formation 4-2-3-1
1McGregor
2Tavernier6Goldson26Davies31Barisic
8Jack4Lundstram
30Sakala37Arfield14Kent
9Colak
1McGregor2Tavernier6GoldsonSubstituted forKingat 45'minutes26Davies31Barisic8JackSubstituted forDavisat 60'minutes4Lundstram30SakalaSubstituted forMatondoat 76'minutes37Arfield14KentSubstituted forWrightat 76'minutes9ColakSubstituted forMorelosat 76'minutesSubstitutes
3Yilmaz10Davis17Matondo19Sands20Morelos23Wright28McCrorie33McLaughlin38King44Devine71TillmanLiverpool
Formation 4-4-2
1Alisson
2Gomez5Konaté4van Dijk21Tsimikas
19Elliott14Henderson3Fabinho28Freitas Gouveia Carvalho
9Firmino27Núñez
1Alisson2GomezBooked at 90mins5KonatéSubstituted forMilnerat 79'minutes4van Dijk21TsimikasSubstituted forRobertsonat 68'minutes19Elliott14HendersonSubstituted forThiago Alcántaraat 67'minutes3Fabinho28Freitas Gouveia Carvalho9FirminoSubstituted forJotaat 73'minutes27NúñezSubstituted forSalahat 68'minutesSubstitutes
6Thiago Alcántara7Milner11Salah13Adrián20Jota26Robertson43Bajcetic47Phillips62KelleherLive Text
Match ends, Rangers 1, Liverpool 7.
Second Half ends, Rangers 1, Liverpool 7.
Attempt blocked. Ben Davies (Rangers) left footed shot from outside the box is blocked.
Corner, Rangers. Conceded by Thiago.
Joe Gomez (Liverpool) is shown the yellow card for a bad foul.
Foul by Joe Gomez (Liverpool).
Alfredo Morelos (Rangers) wins a free kick in the attacking half.
VAR Decision: Goal Rangers 1-7 Liverpool (Diogo Jota).
Goal! Rangers 1, Liverpool 7. Harvey Elliott (Liverpool) right footed shot from the centre of the box to the bottom left corner.Goal awarded following VAR Review.
Corner, Liverpool. Conceded by Leon King.
Foul by Thiago (Liverpool).
Scott Wright (Rangers) wins a free kick in the defensive half.
Goal! Rangers 1, Liverpool 6. Mohamed Salah (Liverpool) left footed shot from the right side of the box to the bottom left corner. Assisted by Diogo Jota.
Goal! Rangers 1, Liverpool 5. Mohamed Salah (Liverpool) left footed shot from the centre of the box to the bottom right corner. Assisted by Diogo Jota.
Substitution, Liverpool. James Milner replaces Ibrahima Konaté.
Foul by Virgil van Dijk (Liverpool).
Alfredo Morelos (Rangers) wins a free kick in the attacking half.
Substitution, Rangers. Scott Wright replaces Ryan Kent.
Substitution, Rangers. Rabbi Matondo replaces Fashion Sakala.
Substitution, Rangers. Alfredo Morelos replaces Antonio-Mirko Colak.
