Philippe Coutinho, with the first hat-trick of his Anfield career, Roberto Firmino, Sadio Mané and Mohamed Salah were all scored on the scoresheet as Liverpool struck seven without reply for the second time in the group campaign.
A Liverpool win would not only see them through as winners of the group, but it would also be the first time any single country has sent five teams through to the knockout stages.
Spartak allowed Liverpool's attacking trident far too much space and they took full advantage in the 15th minute with a super team goal as Mane fed Salah, who slipped the ball inside to Firmino to set up his compatriot, Coutinho, for a simple finish.
Liverpool were at their free-flowing best as they saw off Spartak Moscow at Anfield to claim top spot in Group E.
"They've got people with pace, they all score goals. They looked both really well", Klopp said ahead of the game against the Russian club, as quoted on Liverpool's official site.
Liverpool's early onslaught began from the spot, Coutinho coolly sending the goalkeeper the wrong way after Salah had been dragged down by Giorgi Jikia.
Three minutes later, Liverpool added their third.
In the 85th minute, Salah finally got his long-sought goal after receiving the ball inside of the box, fakes a shot that led two defenders to collide with each other before shooting with his right foot straight into the top corner. Milner delivered an inviting cross for Mane to thump home on the volley less than two minutes into the second half.
Keane said: "A comfortable night for them tonight, a good start and their attacking players certainly enjoyed it".