The Foxes began life without Claudio Ranieri in impressive style, scoring three goals in the opening hour and holding out with ease for their first victory of 2017.
It was another disappointing night for Jurgen Klopp and his Liverpool side, meanwhile, who have now won just two of their last 12 outings in all competitions and missed out on the chance to climb up to third this evening.
Crosses into the box were proving tough for the Reds to deal with, and it was from another uncleared direct throw that Jamie Vardy put his foot through the ball and came close to making the breakthrough.
The ball took a deflection off Shinji Okazaki - the only player to come into the side from last time out - and forced a big stop out of Mignolet down to his left.
Huth sent another header over the bar as a first half largely dominated by the hosts transpired, and the key opener eventually arrived prior to the half-hour mark after Marc Albrighton slotted through Vardy, who made no mistake in tucking past Mignolet in a move reminiscent of the Leicester side of 2015-16.
Mignolet, who had kept out Vardy from close range soon before that opener, was becoming increasingly busier as he was made to keep out a well-struck Wilfred Ndidi shot from 10 yards out.
Leicester, previously without a goal this calendar year, were in dreamland 39 minutes in when Danny Drinkwater bagged their second of the evening, superbly picking out the bottom corner from range on the half-volley after James Milner only half-cleared a cross into the box.
Liverpool failed to offer any real response in the remainder of the first half, coming closest to finding a route back into the game when Emre Can's curler was pushed wide by Kasper Schmeichel on the brink of the interval.
The Reds, on the end of just one defeat in their last nine meetings between these sides prior to tonight, did manage to step things up in the second half as their opponents sat back.
Philippe Coutinho had one shot turned away by Schmeichel, but Liverpool's pressure amounted to little and it was the Foxes who bagged the third of the match on the hour.
Liverpool did manage to grab a foothold in the match soon after through Coutinho, who picked his spot following some good work from Roberto Firmino to give his side just a glimmer of hope with his first goal in 12 games.
Fuchs and Drinkwater both fell short with their latest attempts, while substitute Ben Woodburn was just about thwarted by Schmeichel up the other end, meaning a turbulent week for City ended on a high with three vital points.