Coutinho opened the scoring after just four minutes from the penalty spot after Mohamed Salah was fouled by Georgi Dzhikiya.
The Brazilian grabbed his second on 15 minutes after being set up by Roberto Firmino, who added a third himself soon after.
Liverpool went into the break with a 3-0 lead and Sadio Mane hit the hosts' fourth two minutes after the restart, with his sublime volley the pick of Liverpool's seven goals.
A deflected shot soon after saw Coutinho complete his hat-trick, with Mane scoring his second and the Reds' sixth before Salah completed the scoring to condemn Spartak to a demoralising loss on Merseyside.
Th victory ensured Liverpool finished at the top of the pile in Group E, while Spartak will enter the Europa League draw after finishing third.