The Reds led in the 15th minute when Divock Origi flicked in from close range before Roberto Firmino made it 2-0, heading in Nathaniel Clyne's cross.
Origi also went close when his low shot was saved by Stephen Bywater.
Tom Naylor inadvertently put the ball in his own net after the break before Daniel Sturridge tapped in his first and then thumped home the Reds' fifth.
Liverpool manager Jurgen Klopp made only four changes from the XI that started in the 2-0 league defeat at Burnley on Saturday.
The quality of the visiting team was soon apparent at the Pirelli Stadium against a Burton side who have had a mixed start to their first ever season in the Championship.
After Liverpool's Belgian forward Origi cleverly profited from tricky work in the box from Sadio Mane, Brazilian Firmino doubled the lead following a terrible throw-out from goalkeeper Bywater.
It was 3-0 just after the hour when the unfortunate Naylor had little time to react as James Milner's ball came towards him at pace.
And substitute Sturridge then grabbed a late double, converting at the far post from Milner's pass before firing in low from 15 yards.
Liverpool manager Jurgen Klopp: "There were still a few situations where we were missing a bit of sharpness but the main problem was, it was unbelievable, our build-up and style of play at Burnley - one more pass but 15 times we are completely free in the box.
"So we needed to use this game and that's what we did and it was better."
Burton manager Nigel Clough: "It's difficult for our lads to compete with that sort of quality. With this being 72 hours before the Derby game, our focus was always with that one.
"When you think we finished with a couple of teenagers and a 20- or 21-year-old, you could train with them for a couple of seasons and not gain the experience they've got tonight."
A strong Liverpool side overwhelmed Championship outfit Burton Albion to reach the EFL Cup third round.