The visiting Foxes went ahead after Kasey McAteer rounded off some superb play from Enzo Maresca's men, giving the Championship leaders on a shock lead on Merseyside.
After going into half-time behind, Jurgen Klopp saw an admirable response from his troops in the second period, with goals from Cody Gakpo, Dominik Szoboszlai and Diogo Jota securing the hosts' passage into the last 16 of the competition.
Liverpool commenced their domination of possession at Anfield from the offset, however it was Leicester who went ahead in the third minute after a brilliant counter-attack.
Kostas Tsimikas was dispossessed quite some way into the Foxes' half, prompting a swift break forward from Yunus Akgun who slotted the ball into the path of the onrushing McAteer.
The young winger composed himself with only the Reds' goalkeeper to beat, and the 21-year-old kept his cool to slot past Caoimhin Kelleher in the Liverpool net.
Delighted to have grabbed a lead to protect at Anfield, the Championship leaders defended resolutely for the remainder of the first period, although Maresca's men had the crossbar to thank after 12 minutes.
A dangerous-looking ball from the left was met by Ben Doak at the back post, however the academy graduate was unable to keep his effort on target, striking the frame of Leicester's goal.
Former Everton Conor Coady did his fair share of defensive work to maintain the Foxes' lead, with the Englishman clearing Gakpo's header off the line only moments following Doak's miss.
Reds boss Klopp would have had some words of encouragement for his men in the dressing room during the half-time interval, and whatever the German said paid dividends just three minutes after the restart, with Liverpool's Dutch midfielder getting on the scoresheet.
Summer arrival Ryan Gravenberch did well to pick out Gakpo in the 18-yard box, where the former PSV Eindhoven man found an inch of space to execute a low-drilled strike past Jakub Stolarczyk in the Leicester net.
Following Liverpool's first of the match, the momentum had completely swung in the hosts' favour, and a quick start off the bench from Szoboszlai gave Klopp's charges the advantage in the contest.
Just five minutes after entering the field of play, the Hungarian was found by midfielder Wataru Endo in considerable space on the edge of the box, and the former RB Leipzig playmaker rifled a thunderous effort into the top-left corner.
Despite having a lead to protect, the Premier League side still looked susceptible in transitions, with Wilfred Ndidi running through on goal before being halted by the Liverpool defence.
The Reds made sure of their place in round four of the competition in the 89th minute, when centre-back Jarell Quansah did well to shrug James Justin off the ball before passing to Jota, who produced a delicate-flicked finish that dribbled into the Leicester goal.
Liverpool have now won all of their last four matches by a scoreline of 3-1, and the Merseysiders will be looking to extend their unbeaten run at the start of this term to nine matches when they travel to Tottenham Hotspur on Saturday in the Premier League.
Maresca's Foxes only have second-tier matters to focus on until January after their elimination from the EFL Cup at Anfield - the Championship leaders travel to Blackburn Rovers on Sunday afternoon.