This is what Liverpool can do. This is why Jurgen Klopp was brought to Anfield. And this is why, as long as the German stays, there will always be hope that something special may eventually be built on Merseyside.
There are currently flaws in Klopp's grand design. The Premier League table tells us that.
But here on a cold Anfield night were the exhilarating basics of the Klopp prototype. Energetic, intuitive, hypnotic passing football with a devastating cutting edge.
Liverpool made the perfect start with Philippe Coutinho's early penalty after Mohamed Salah was pushed to the ground
Coutinho doubled the advantage after a sweeping move, finishing into the bottom corner after a Roberto Firmino pass
It was 3-0 after just 18 minutes when Firmino capitalised on a defensive error to finish instinctively against Spartak Moscow
Sadio Mane added the fourth goal three minutes after half time with a powerful volley from a perfect James Milner cross
Coutinho completed his hat-trick just two minutes after Mane's goal, in front of the Kop, with a heavily deflected shot
Mane added goal No 6 with a back-heel flick following a low cross by second-half substitute Daniel Sturridge
Salah was only member of Liverpool's 'Fab Four' not to score until he slammed into the roof of the net with five minutes left
MATCH FACTS, RATINGS, MATCH ZONE AND TABLE
LIVERPOOL (4-3-3): Karius 6.5; Gomez 6.5, Lovren 6.5 (Alexander-Arnold 60min, 6), Klavan 6.5, Moreno 6 (Milner 45, 6.5); Coutinho 8.5, Can 7.5, Wijnaldum 7.5; Salah 8, Firmino 7.5 (Sturridge 72, 6), Mane 7.5.
Subs not used: Mignolet, Henderson, Oxlade-Chamberlain, Solanke.
Scorers: Coutinho 4 (pen), 15, 50, Firmino 18, Mane 47, 76, Salah 86.
Manager: Jurgen Klopp 8.
SPARTAK MOSCOW (4-2-3-1): Selikhov 5; Eschenko 5, Tasci 5, Bocchetti 5, Dzhikiya 6 (Pasalic 60, 6); Glushakov 6, Fernando 6.5; Zobnin 6, Luiz Adriano 5, Promes 5 (Samedov 75, 6); Ze Luis 5 (Melgarejo 51, 5).
Subs not used: Rebrov, Kutepov, Popov, Rocha.
Booked: Dzhikiya, Fernando.
Manager: Massimo Carrera 5.
Referee: Szymon Marciniak (Pol) 7
All of Liverpool's 'Fab Four' - Mane, Salah, Firmino and Coutinho - were all involved in the build up to their second goal. For more facts and stats, visit our exclusive MATCH ZONE service by clicking here.
SEVILLA GO THROUGH
Sevilla stuttered into the last 16 of the Champions League after being held to a 1-1 draw by Group E's bottom side Maribor.
Liverpool's convincing victory over Spartak - the Spanish team's rivals for second place - ensured that even after dropping points, they progressed to the knockout stage.
Marcos Tavares stunned the Spaniards with the opening goal after 10 minutes, heading home Martin Milec's cross from close range.
In a one-sided second half, Sevilla breached the stubborn home defence when goalkeeper Jasmin Handanovic failed to keep out substitute Ganso's low shot following good work by Joaquin Correa.
Maribor, the Slovenian champions, were already consigned to bottom place after scoring two goals in five group matches before this, their third draw in the competition.
Liverpool's football could have sliced open a sealed envelope and would not have looked any prettier had it been painted in watercolour. It was terrific to watch and for the Russians of Spartak Moscow it proved impossible to play against.
That much was evident in the scoreline. Spartak are the champions of Russia and as such are no mugs. But their credibility was swept away on a night when Klopp's team took their goal tally in qualifying to a staggering 23. This is a record for an English team in Europe.
To say Liverpool are on a decent run of goals is like saying Australia may be slight favourites for the Ashes. They have scored 33 times in their last 10 games — beginning with their 7-0 victory away at Maribor in this competition.
'Nobody could have imagined this,' said Klopp on Wednesday night. 'It was an all-or-nothing night for both teams but we started perfectly and showed that we are really difficult to play against when we go into the next gear.'
Liverpool's journey through Group E had already shown us the best and worst of them. They scored three in the first half at Sevilla recently but still drew the game.
So Liverpool had to win on Wednesday to top the group and draw to make sure they went through to the next round. So, in theory, it could have been a nervy affair.
Instead it was 90 minutes of gilded Liverpool football, a night Spartak were embarrassed and dismantled by the kind of devastating passing play that is only possible when you are blessed with a certain kind of player.
Liverpool needed a win in order to qualify and were given a huge chance after four minutes when Salah was pushed over
Coutinho tucked away the penalty with ease to set Liverpool on course for the Champions League knock-out stages
Liverpool needed a win to go through as group winners, and went 2-0 up when Coutinho finished into the bottom corner
Coutinho was named captain for the Wednesday night game and led by example with two well taken finishes at Anfield
Here, the four leaders of Liverpool's orchestra were all present and in tune. Brighton manager Chris Hughton suggested after his team conceded five at the weekend that Philippe Coutinho, Roberto Firmino, Mo Salah and Sadio Mane are a match for Pep Guardiola's forward players at Manchester City.
Many people scoffed but here was evidence to at least provoke a credible discussion.
Spartak needed to start well but didn't. They needed to still be in the game at half-time as that is when Liverpool can grow nervy. But the Russians gave away a needless penalty when Georgi Dzhikiya hauled down Salah in the third minute and Coutinho scored to set Liverpool on an upward trajectory.
For a while all the football flowed one way. Spartak were hustled from their stride by Liverpool's hungry pressing and a superb passing move involving Mane, Salah and Firmino allowed Coutinho to sidefoot his second goal in only the 15th minute.
Victory, which was all but secured inside 20 minutes with Firmino's goal, ensured five English teams get into the last 16
It is the first time a nation has had so many teams through to the knockouts, and Liverpool showed why they should be feared
Mane got in on the goal scoring act in some style, acrobatically volleying past Alexander Selikhov from around 10 yards out
Mane celebrates his goal as Spartak proved completely unable to deal with Liverpool's attack; they go into the Europa League
Spartak were back in to the self-harm routine four minutes later when Denis Glushakov gave the ball away in midfield and Mane crossed for Firmino to finish skilfully on the half-volley after the ball dropped from the shoulder of Spartak's Serdar Tasci.
With the game all but won, Liverpool missed chances and looked as though they may coast through the second half ahead of a Premier League meeting with Everton this weekend.
But Salah set the tone for a second half of even greater punishment with a soaring scissor-kick immediately after the restart that would have torn the net from its rigging at the Kop End had it been struck a fraction harder.
As the night wore on, Liverpool's enduring thirst for more was matched only by the flawlessness of some of their technique.
Coutinho's hat-trick goal was a little fortunate — taking a deflection — but Liverpool cut Spartak open brutally again with 14 minutes left.
Coutinho's third took a huge deflection off Salvatore Bocchetti and wrong footed the completely overworked Selikhov
Coutinho celebrates his third goal - it was Liverpool's 21st in the group stage, a record number for a Premier League club
Such was Liverpool's dominance and good fortune, Mane was able to score even from the ground with the ball behind him
Liverpool threw down a major warning to rivals Everton ahead of their Premier League derby clash at the weekend
Emre Can sent Daniel Sturridge away and Mane dragged the ball into the empty goal from six yards as the substitute's selfless cross threatened to pass just behind him.
Great players always have time when they are in a good place and that was the way it was here.
Coutinho and Firmino had already stroked balls into the goal as though they were taking part in a passing drill and Salah went about things the same way after leaving a defender on the seat of his pants with the latest in a series of adroit turns in the 85th minute. Teams are not supposed to score seven in Europe. The competition is supposed to be too tight.
But Liverpool can do special things when the mood takes them and, right now, Klopp has his team pointed towards opportunity.
On nights like this it is hard to imagine that we would ever doubt him.
Salah had all the time he needed to control and finish into roof of the net as Liverpool won 7-0 for the second time in the group
Liverpool, having beaten the English record for group stage goals, then took the overall record set by PSG this season
Liverpool suffered a blow before half-time when Alberto Moreno went off injured to be replaced by James Milner at left back
Moreno was comforted by his team mates as he hobbled off - the Spaniard is now a doubt for the weekend's Merseyside derby
Another blot for Liverpool came when Emre Can got an early booking, meaning he misses the first leg of their last 16 match
Milner hurdles a challenge - he took the captain's armband from Coutinho at half-time after coming off the bench
Despite Liverpool's superb display, manager Jurgen Klopp was his usual demanding and vocal presence on the touchline
A Liverpool fan looks suitably festive while still wearing her club's colours as she sings 'You'll Never Walk Alone' pre-match