A Coronavirus outbreak forced Villa to field an entirely youthful side, whilst the Reds pulled out the big guns in Fabinho, Georginio Wijnaldum, Mohamed Salah and Sadio Mane amongst others.
Villa trailed in the first four minutes after Mane got on the end of a teasing ball at the near post of the six-yard area from Curtis Jones to head into the bottom-corner.
Fabinho could've made it two midway in the first half from a first-time strike at the back-post following a corner-kick, but Akos Onodi parried before Mane sent the follow-up across goal.
The Clarets, who slowly began to find their feet, levelled five minutes to halftime when Louie Barry beat the offside trap before going on to find the bottom-corner.
Jones nearly restored Liverpool's lead a minute before the interval through a curling strike from outside the area, but it was beaten away by Onodi.
Liverpool manager Jurgen Klopp issued a change at start of the second half, Thiago Alcantara replacing Jordan Henderson.
The Reds regained the lead on 60 minutes when Wijnaldum picked up a cutback on the edge of the area from Takumi Minamino to drill home a composed finish.
A goal-feast materialised in just three minutes as Mane leaped towards a ball from the right to send a looping header into the far corner of Onodi's net.
Salah got in on the act two minutes later when the Egyptian collected a low pass on the shoulder of the area from Xherdan Shaqiri to find the near corner of the net.
Liverpool, who could've added to their tally following the closing minutes, ran down the latter phases to confirm their spot in the next round.