The five-times European champions took the lead in the fourth minute with a Coutinho penalty after Salah was pulled down by Georgi Dzhikiya.
Vincent Aboubakar scored twice for the Portuguese club, with Yacine Brahimi, Alex Telles and Francisco Soares also netting.
Spartak's defending was as desperate as Liverpool's attacking was dazzling and a clumsy touch by Serdar Tasci opened the door to a third goal. And with qualification for the knockout rounds at stake, this was definitely an occasion where the Liverpool team needed their fans behind them.
The 27-year-old is no longer a guaranteed starter. "It's a little bit cold so people need to move!"
"I'm a numbers man when it comes to creativity and when it comes to Coutinho - they're not great you know". Before Salah smashed in the seventh four minutes from time.
"We opened the game perfectly and after we took the lead we didn't have to defend".
Sam Allardyce has left the bulk of his kept the bulk of his first-team at Finch Farm, giving little credence to Everton's Europa League dead rubber against Apollon Limassol, but Jurgen Klopp cannot afford that luxury. Even so, there's no doubt they have given themselves a better chance of progressing deeper into the tournament having clinched top spot, with Paris Saint-Germain and Barcelona both lurking as possibilities had they slipped up and finished second and fewer alternatives to help avoid the big fish.
Half time was a welcome break for the Muscovites, but their torment was to resume in the second half.
"That is to make two or three changes every game and rotate and freshen the team up". They just steamroll teams with their energy, with the fab four as we call them.
Cristiano Ronaldo set a Champions League record by scoring for Real Madrid in their 3-2 win over Borussia Dortmund, becoming the first player to find the back of the net in all six group games.
Needing only a draw to qualify, it was all too easy for Liverpool at Anfield, where Coutinho led Liverpool's dismantling of Spartak with two goals in the opening 15 minutes before completing his first hat trick for the Reds in the 50th.
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