The young Reds controlled the Group G tie at Chester FC for long periods and took the points courtesy of Bobby Adekanye’s first-half brace and goals after the break from Toni Gomes and Harry Wilson.
Victory increased Neil Critchley’s side’s points tally to seven in the section, with trips to Bristol City and Stoke City ahead of them next month.
After the opening 10 minutes passed by with little action of note, Liverpool seized control of the game en route to going in front.
Gomes sent a header onto the outside of the left post from Adekanye’s cross before Yan Dhanda’s drive was repelled by Charlton goalkeeper Ashley Maynard-Brewer.
The ever-influential Wilson almost put one on a plate for Adekanye after completing a rapid one-two with Dhanda and sweeping the ball towards the back post, but the No.11 could not convert.
But the former Barcelona forward did break the deadlock in the 19th minute.
A similar move began with Ovie Ejaria sending a pass out to the right for Dhanda, who served a fine assist across the area for Adekanye to make amends from close range.
Herbie Kane blasted a brilliant effort from 25 yards that was destined for the top corner until Maynard-Brewer clawed it clear, while Brandon Hanlan reminded the Reds that their lead was slender when he ran through and swerved a curler just off target.
But the cushion Liverpool deserved was reflected in the scoreline on 39 minutes.
Kane picked out Adekanye with an excellent diagonal delivery from outside the box and the winger met the cross with a coolly-taken header back past the ‘keeper into the bottom corner.
Maynard-Brewer was at full stretch to palm out another angled Dhanda effort in the closing stages of the first half – and there was still time for the visitors to halve their deficit in stoppage-time.
Charlton stole possession at the edge of the Liverpool area and Louis-Michel Yamfam sped into shooting territory and dragged a finish beyond Caoimhin Kelleher.
LFCTV GO: Watch the highlights from the 4-1 win
Any hopes the young Addicks had of mounting a comeback were put to bed when the Reds grabbed a quickfire double early in the second half, however.
Wilson’s hard pressing in the opposition half forced an error that allowed Kane to lure out the ‘keeper and roll the ball square to Gomes for a straightforward strike into an open net.
And on 53 minutes it was four. Wilson raced onto a long pass over the Charlton defence and when Maynard-Brewer rushed out, the Welshman delicately lofted a finish home.
A deluge of rain did not deter either side from pressing for goals. Gomes worked Maynard-Brewer at one end, while Terrique Anderson pulled a low hit wide on the counter and then had a strong shot punched away by Kelleher at the other.
But the day’s scoring was done and Liverpool’s Premier League Cup ambitions received a timely boost with two games left to play in the group.
Liverpool U23s: Kelleher, Masterson, Juanma, Johnston, Alves (Longstaff, 33), Kane, Dhanda, Ejaria, Gomes, Wilson, Adekanye.
Unused substitutes: Sharif, Grabara, Glennon.