A Roberto Firmino brace, either side of James Milner's penalty, was followed by a low drive from Trent Alexander-Arnold in the Reds' 17th win in 18 top-flight outings in 2019/20.
A raucous Filbert Way atmosphere greeted the two sides at kick-off, but it was the reigning European and world champions who started the brightest in a clash of the top two.
Alexander-Arnold forced a smothered save from Kasper Schmeichel inside the opening 60 seconds while Sadio Mané and Mohamed Salah missed the target early on.
Schmeichel also did well to distract Salah when the Egyptian broke and found space in Leicester's half before firing it into the side netting, largely due to the presence of City's No.1
Jamie Vardy, the Premier League's top scorer, had a half-chance to give the Foxes an early lead, however his effort was blocked, and it was Liverpool who looked most likely.
They did go ahead in the 31st minute as Alexander-Arnold floated a perfect cross for Firmino at the far post and the Brazilian duly obliged to nod it past Schmeichel.
The Dane was needed to make a brilliant stop to deny Mané again shortly after the opener, getting a firm hand to the Senegalese's effort, after the Reds broke free again.
Leicester carried an increased threat after the interval and Youri Tielemans had an 18-yard shot deflected behind for a corner while the home side were also pressing higher.
Schmeichel made another excellent save to prevent Salah from making it two on 56 minutes, tipping the 27-year-old's strike onto the crossbar, although Firmino was offside beforehand.
Maddison and Praet both had chances for the Foxes, but when Çağlar Söyüncü was adjudged to have handled the ball in the area, the Merseyside outfit were awarded a penalty.
Substitute James Milner stepped up to convert for the Reds before Firmino's close-range finish and an excellent low drive from the impressive Alexander-Arnold made it 4-0.
Midfielder James Maddison looks to get forward.
While Liverpool were dominant throughout on Filbert Way, James Milner's penalty with 19 minutes to go was the first of three goals in quick succession for the visitors.
Up until that point, with the score at just 1-0, it remained possible for Leicester to gain a foothold in the game, but Milner's spot-kick afforded the Reds with a two-goal cushion to push on.
The Nigeria international midfielder challenges Roberto Firmino for possession.
Matt Elliott told LCFC Radio: "It’s a tough decision. It hasn’t been vintage Leicester tonight, but that’s largely down to the opposition, isn’t it? No one has really stood out, but I think Wilfred Ndidi has battled away. In the heart of midfield, he’s had a big task, but he hasn’t given up."
Where does it leave us?
Under pressure from Andrew Robertson, Ricardo Pereira gets the ball forward.
The Foxes remain second in the Premier League, but are now 13 points behind leaders Liverpool, who also have a game in hand against West Ham United.
Champions Manchester City are a point adrift of Leicester, meanwhile, and they travel to Molineux to tackle Wolverhampton Wanderers on Friday.
The Premier League's top scorer looks to get an effort away against the Reds.
Leicester are in Premier League action on Saturday when they head to London Stadium to face West Ham United (5:30pm kick-off).
They then visit St. James' Park on New Year's Day for a clash with Newcastle United in a 3pm kick-off in the North East.
All times GMT.
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