The Foxes capitalised upon an inspired start when Jamie Vardy ended their 637-minute wait for a Premier League goal, latching on to Marc Albrighton's through ball and finishing confidently.
Danny Drinkwater's sumptuous 25-yard half-volley doubled a rampant Leicester's lead before Vardy sealed his brace on the hour mark to put the hosts well in command.
Philippe Coutinho's controlled strike pulled one back for Liverpool on 68 minutes, but they couldn't build upon it to mount a comeback, instead suffering another huge setback in their hopes for a top-four finish.
Leicester meanwhile lifted themselves two points clear of the relegation zone, with interim manager Craig Shakespeare increasingly likely to be given the rest of the season in charge of the reigning champions.
Shakespeare makes single change in first game in charge
With Ranieri - who remarkably led the Foxes to the title last term - controversially sacked last Thursday as a result of Leicester's recent slide, Shakespeare took responsibility over the starting line-up for the first time.
Shinji Okazaki was the interim manager's only change from last week's Champions League last 16 first-leg defeat away to Sevilla, replacing Ahmed Musa up top.
Jürgen Klopp's Liverpool themselves made just the one change from their win over Tottenham Hotspur a fortnight ago, Emre Can taking the place of Jordan Henderson in midfield with the captain out with a bruised foot.
Dejan Lovren's continued absence with a knee injury meant Lucas Leiva partnered Joël Matip in central defence, while Daniel Sturridge again missed out altogether with a virus.
Strong start sees Leicester go close on a number of occasions
Leicester came into this game having lost their last five successive games and as the only side in England's four divisions - and even Europe's top five leagues - yet to score a league goal in 2017.
In response, Shakespeare returned to what he called a "tried and trusted" set-up, adopting a 4-4-2 formation with Okazaki in behind Vardy and 10 of the regular 11 players that took them to the title last term all starting.
Backed by a boisterous home support, the Foxes started strongly with Simon Mignolet having to catch Robert Huth's knock-on header after Christian Fuchs' long throw from the left inside five minutes.
And Mignolet was forced to push Okazaki's header wide of the post quickly after, as the Japan international flicked on Vardy's bouncing volley with his back to goal.
Liverpool struggled to gain a foothold due to Leicester's intensity and tempo, though captain Wes Morgan had to be on hand to clear Sadio Mané's low cross after a flowing forward move.
The Reds were fortunate Robert Huth could not get over the ball as slack marking allowed him a clear run towards the ball at a corner - only for the towering German to power his free header high over the crossbar.
Leicester's energy and confidence, that they lacked so badly under Ranieri, meant a breakthrough seemed inevitable. They went close again on 20 minutes when Vardy pulled down a long ball with an excellent first touch but fired his volley straight at Mignolet from six yards after spinning Matip.
Vardy brings long-awaited league goal
But Leicester finally ended their long wait for a top-flight goal before the half-hour, Vardy scoring his first Premier League goal since firing a hat-trick in a 4-2 home win over Manchester City back in December.
Marc Albrighton's sublime first-time through ball sent Vardy through one-on-one and undaunted by his barren domestic run, the striker fired inside Mignolet's near post for Leicester's first league goal in 637 minutes and only his second goal in his last 19 league outings.
Leicester having won all five of the league games in which they had scored first in prior to this, Liverpool's task was set - but they initially responded well as Kasper Schmeichel had to come off his line to thwart Coutinho following another good attacking move.
Yet Leicester continued to cause chaos among Liverpool's back-line, Vardy breaking beyond Lucas before setting up Wilfred Ndidi - though Mignolet denied him with a strong two-handed stop.
Drinkwater stunner doubles Foxes' lead
But on 39 minutes it was 2-0 to Leicester when James Milner's headed clearance fell to Drinkwater on the edge of the box and the midfielder lashed a spectacular half-volley with the outside of his right foot that curled away from Mignolet and into the bottom right corner.
Schmeichel pushed Can's strike wide of the post as Liverpool looked to summon a response before the break, but Klopp's charges were woefully substandard and deserved little else.
Klopp switched to a back three with Can joining the struggling Lucas and Matip as he looked for his Liverpool side to combat a dire first-half which belied the fact they enjoyed a 16-day break between this and their last fixture.
Yet while Liverpool enjoyed greater control of the ball, they failed to test Schmeichel enough - the Dane easily catching Coutinho's low attempt from range.
Vardy brace puts Leicester well in command
And on the hour mark, Liverpool were made to pay as Leicester stretched their lead to three - Fuchs' cross picking out Vardy in the middle with the striker leaping above Can and flicking a header into the bottom corner.
Matip fired into the side-netting from distance before Lallana had a strike beaten away by Schmeichel as Liverpool went close.
But they finally pulled one back on 68 minutes, Can riding Danny Simpson's challenge and cutting inside for Coutinho to roll into the bottom corner for his first goal since November 6th.
That rubbished Leicester's hopes of a first clean sheet in 11 games and injected some urgency to Liverpool's play, but the home side's switch to a 5-4-1 with Daniel Amartey replacing Okazaki made it difficult for them to create any more chances.
Can had cries for a penalty go unanswered from referee Michael Oliver after Ndidi's clumsy aerial challenge before substitute Divock Origi fired wide as Liverpool continued to toil.
At the other end Drinkwater fired over after good work from Riyad Mahrez as Leicester failed to kill the game off.
Schmeichel almost spilled Coutinho's effort from a Nathaniel Clyne rabona cross into the back of the net, but Leicester ultimately held on to move two points clear of the drop zone with Crystal Palace slipping into the bottom three.
Defeat meanwhile leaves Liverpool fifth, a point behind their next opponents Arsenal who have an extra game to play, the Merseyside outfit having still only won one league game in 2017.