Jurgen Klopp's side dominated the opening period, with goals from Divock Origi and Roberto Firmino giving them a two-goal advantage.
Liverpool lacked the same intensity in the second period, but the goals didn't stop flowing with Luke Naylor and a Daniel Sturridge brace sealing the result and passage into the next round.
Starting off right
After their 2-0 defeat to Burnley at the weekend, Klopp will have expected a response from his players, and they started the game brightly.
Origi tested the waters with an early effort, but an 10th minute attempt from Firmino was the one that really tested Nigel Clough's side.
Adam Lallana did well to take pace off the ball to dink it into the area, which seemed perfect for a unmarked Firmino but decided to head towards the near post which proved easy for Stephen Bywater to save.
It didn't take long for Liverpool to take the lead, with Origi firing home in the 14th minute. James Milner did well to get the ball to the by-line and clipping the ball over to Sadio Mane, he showed great trickery to get beyond the defender and find Origi who flicked home with his heel in some style.
Taking control of the game
The flood gates seemed to open from there, as Liverpool added a second just after the 20-minute mark.
It was a poor clearance from Bywater who threw it straight to Mane, he did well to sense the run of Nathaniel Clyne, whose great cross was easy for Firmino to head home.
The small Liverpudlian contingent inside the Pirelli Stadium, thought they had a third, when Origi looked to have caught out the Burton defence with the run before finding Mane at the back post, but the offside flag was raised quickly.
All wrapped up
The Reds didn't go into the second half with the same intensity, but wrapped up the tie on the hour mark with their third goal.
It was moment to forget for Naylor, as a dangerous corner from Milner proved difficult to defend, and cross cannoned of Naylor and into the net.
Chances were few and far between for the home side, but were handed a golden one when Lucas Akins took the ball on chest and was baring down on goal. However the angle didn't help, and proved his hindrance as he cannoned the effort over the ball.
Sturridge entered the fray and was quick to make an impact, as he deflected effort proved too much for Bywater who palmed it away.
It didn't take long for the English striker to get his eye in as he added the fourth goal, with some ease.
An attempted clearance from Burton fell to Milner who did well to make it out wide, playing a one-two with Mane before firing a dangerous ball across the face of goal fro Sturridge to tap home at the back post.
It got even better seven minutes from time as he added his second, and Liverpool's fifth.
Mane continued to show why Klopp paid so much for his services, making a good run inside before finding Sturridge. The striker took a touch, before stroking the ball home with some ease into the bottom corner.