There were six changes from the Premier League U18 defeat to West Bromwich Albion Under-18s last weekend, including a return to the starting XI for captain Oliver Ewing after he appeared for City's Under-23s against Tottenham Hotspur Under-23s on Monday.
The visitors fashioned the first attempt when Mateusz Musialowski cut inside and saw his low shot held by Chituru Odunze. Liverpool did take the lead on six minutes as James Balagizi took a touch and found the bottom corner.
Leicester looked to respond instantly with Tawanda Maswanhise carrying the ball down the left and skipping past Conor Bradley before appearing to be taken down by the Reds full-back in the area, but referee Andrey Humphries was unmoved.
Still inside the opening 10 minutes, Kian Pennant pounced on a defensive error to drive through on goal and was thwarted by an excellent save from stopper Harvey Davies, who got a hand to his low strike.
Tyler Morton then volleyed a shot which Odunze had to save with his leg as the away side remained a constant counter-attacking threat. Chances continued to flow at either end with Wanya Madivadua creating the space for Ethan Fitzhugh to take aim and find Davies equal to his sweetly-struck effort.
Meanwhile Max Woltman sprung the offside trap and looked to have a clear route to goal until Brandon Cover charged back to block his goal-bound shot, before Reds skipper Jarell Quansah headed the resulting corner over.
Liverpool had another opportunity to double their advantage before the break but Morton got his shot all wrong, skying it over the crossbar, ahead of Madivadua firing wide of target for City.
The visitors came out quickly in the second half and, when Corness played through Musialowski, his shot from a tight angle had to be parried away by Odunze.
City crafted, arguably, the move of the match soon after as Ewing pinched possession on the edge of his own area and exchanged a quick one-two with Braybrooke before finding Maswanhise, who did brilliantly to move forward and pick out Fitzhugh.
He just had Davies to beat but the 'keeper produced a brilliant save to deny him from close range.
Fitzhugh had another effort blocked by Quansah and Leicester kept the pressure on as Braybrooke hit one over the bar from Maswanhise's lay off, while Ewing also saw his volley go narrowly off target.
Maswanhise, meanwhile, tried to curl one in himself by cutting inside from the left but got his angles wrong and fired wide. Liverpool then scored a second against the run of play with just over 20 minutes remaining through Woltman.
And with Leicester throwing ever more players forward in an attempt to get back into the contest, the visitors were clinical on the counter attack. Woltman found time and space to stride into the box and tuck the ball beyond Odunze on 72 minutes.
The Foxes were handed a lifeline when Fitzhugh's shot struck the arm of Quansah, who was sliding in to block the shot in the area and the referee pointed to the spot. Ewing stepped up and confidently slotted it into the bottom corner.
The game was increasingly stretched and Odunze was forced into a smart save to keep out substitute Melkamu Fravendorf late on, before Fitzhugh wriggled his way through but couldn't test Davies.
There would be two further goals at the end, but they went Liverpool's way as Balagizi nipped in to slide the ball home after snatching it out of Odunze's grasp, ahead of rounding the 'keeper a minute later and finding the net once more.
Major moment…
The game was still finely balanced at 1-0 and had Leicester taken one of several second-half chances, the closing stages could have been very different. But once Liverpool scored the second, and quickly the third, it became an unassailable lead despite City's late goal and strong overall performance.
Who impressed?
City winger Tawanda Maswanhise was a constant threat for the Liverpool backline, running with pace and power, but was just unable to find the back of the net.
Where does it leave us?
The young Foxes bow out of the competition at the fifth round stage after a valiant effort in Seagrave.
Coming up…
Arsenal Under-18s visit LCFC Training Ground on Saturday 24 April (12pm BST kick-off) in the young Foxes' next Premier League U18 South fixture.
The details…
City: Odunze; Cover (Lindsay 46'), Nelson, Abdulai, Kutshienza (Booth 84'); Maswanhise, Ewing (c), Braybrooke, Madivadua (Wormleighton 71'); Fitzhugh; K. Pennant.
Subs not used: Chibueze, Cook, Russ, Alves.
Goal: Ewing 76'.