Philippe Coutinho helped himself to a first career hat-trick as the Reds set a new goalscoring landmark for English clubs in the Champions League, recording their second 7-0 win of the group stages.
The result sees Liverpool finish top of Group E, while Spartak Moscow are condemned to Europa League football after Christmas having needed a victory to progress on the final matchday.
Liverpool boss Jurgen Klopp named a strong starting lineup despite the Merseyside derby looming on Sunday, with goalscorers Salah, Firmino, Mane and Coutinho all included from the off.
It proved to be a good decision as the attacking quartet ripped Spartak apart in devastating fashion throughout the match, and they wasted little time getting started with Salah being dragged to the ground inside the area by the returning Georgiy Dzhikiya after just three minutes.
Captain-for-the-evening Coutinho stepped up to send Aleksandr Selikhov the wrong way from the penalty spot, scoring Liverpool's fastest ever Champions League goal at Anfield in the process, but the hosts were quickly back on the front foot in search of a second.
Mane slammed one effort into the side-netting before Coutinho drew a routine stop from Selikhov, but the Brazilian would not have to wait much longer for his second of the night and his 50th in a Liverpool shirt.
Coutinho brought up the landmark in some style, putting the finishing touch to a slick team move which saw Mane and Salah combine to find Firmino, who in turn unselfishly laid the ball on a plate for his compatriot.
Two quickly became three as Liverpool all but killed the game off as a contest inside 20 minutes, and this time Firmino got his own name on the scoresheet with a fine outside-of-the-boot finish after the ball had fallen to him inside the penalty area.
The hosts seemed able to cut through the Spartak defence almost at will, and Salah was the next to come close when his effort shortly before the half-hour mark was kept out by Selikhov.
Spartak did pose the occasional threat at the other end with Quincy Promes looking most likely for the visitors, but Liverpool should have added a fourth with just under 10 minutes remaining of the first half when Firmino and Salah stylishly combined to set up Mane, only for the Senegal international to blaze his finish over the crossbar.
Salah was the next to come close with a curling effort which drifted narrowly past the top corner as he tried to get in on the act, but the hosts were forced to settle for only a three-goal lead at the halfway stage.
The Reds squandered a 3-0 half-time advantage in their last Champions League game, but any danger of that happening again was wiped out within two minutes of the restart as Mane added a stunning fourth goal.
James Milner - on for the injured Alberto Moreno in the closing stages of the first half - whipped a cross in from the left which Mane met with a thunderous volley that crashed into the back of the net past a helpless Selikhov.
Promes was trying his best to put up a one-man resistance and forced Loris Karius into a rare save moments later, but it was only a temporary reprieve and Liverpool made it two goals inside three minutes as Coutinho completed his first hat-trick for the club.
Again Milner was the creator as his pass found the Brazilian, whose quick strike took a big deflection on its way past the keeper for Liverpool's 21st goal of the group stages - a new Champions League record for English clubs.
Liverpool's blitz left top-scorer Salah as the only member of the front four yet to find the back of the net, but the Egypt international came close to a 12th goal in his last 11 games when he span away from his marker on the edge of the box and saw his subsequent effort nudged narrowly wide by the fingertips of Selikhov.
Spartak almost registered a consolation with 15 minutes remaining when Promes clipped the outside of the post from the edge of the box, but Liverpool again responded quickly and within two minutes they had their sixth of the evening.
Once again the hosts ruthlessly punished Spartak for giving the ball away in midfield as Salah threaded a pass through for Daniel Sturridge, who in turn put a low cross into the middle which Mane did well to hook in after the ball arrived behind him.
Sturridge came close to adding his own name on the scoresheet late on, but it was Salah who joined the party with the seventh goal as he collected Milner's knockdown before taking his time inside the box and placing a composed finish into the top corner - his 18th of the season across all competitions.
There was no stoppage time as the referee put Spartak out of their misery, leaving Liverpool to celebrate another memorable Champions League victory that secures their place in the knockout rounds of the competition for the first time since 2008-09.
Only Paris Saint-Germain - also this season - have ever scored more goals than Liverpool managed during their group stage, with two 7-0 victories contributing to a final tally of 23 from only six matches.
The Reds will now go into Sunday's Merseyside derby with Everton full of confidence, while Spartak must pick themselves up for a derby of their own as they host city rivals CSKA Moscow in their final match before the three-month winter break.
Liverpool (4-3-3): Karius; Gomez, Klavan, Lovren (Alexander-Arnold, 60'), Moreno (Milner, 45'); Can, Wijnaldum, Coutinho; Mane, Salah, Firmino (Sturridge, 72')
Spartak Moscow (4-2-3-1): Selikhov; Eshchenko, Tasci, Bocchetti, Dzhikiya (Pasalic, 60'); Fernando, Glushakov; Zobnin, Adriano, Promes (Samedov, 75'); Ze Luis (Melgarejo, 51')