The Reds knew they needed three points to qualify and they started in confident mood. Captain Conor Coady led his team from midfield and dictated play from the outset.
Coady opened the scoring from the penalty spot on 30 minutes shortly before Samed Yesil slotted past Dawid Smug to take the home side into the break 2-0 up.
Inter came out fighting in the second half with Marco Benassi finding the net on 61 minutes but Liverpool responded almost immediately with German U21 International Samed Yesil grabbing his second goal on the night with a fine finish.
Ryan McLaughlin won his second penalty of the game 10 minutes from time which Coady converted to end the game 4-1 and send his side through to the last 16.
The result means all but one team have officially qualified for the last 16 - Chelsea will qualify should they avoid a 12-goal defeat away to Ajax later this month.