On Thursday evening, the visitors got off to a flying start against the second-place Foxes, dispelling any idea that Jurgen Klopp's side would be fighting fatigue after their triumph at the Club World Cup in Qatar, reports Efe news.
The Reds have taken 52 of a possible 54 points from 18 matches.
The Manchester United supporters, who packed into Old Trafford on Thursday for a clash with Newcastle United, were rewarded with one of the Red Devils' finest performances of the season as the hosts romped 4-1.
With the win, Man United have 28 points from 19 matches and occupy the 7th spot on the Premier League table.
In the first of the Boxing Day fixtures, Tottenham Hotspur came from behind to beat Brighton & Hove Albion 2-1 and take some of the sting out of last weekend's loss to Chelsea.
Spurs' sixth victory in nine matches under new coach Jose Mourinho left the London side with 29 points from 19 matches and they are now fifth in the Premier League, three points behind Chelsea.
Tottenham archrivals Arsenal traveled to the South Coast to face 16th-place Bournemouth in the Gunners' first outing with Mikel Arteta in charge and were held to a 1-1 draw.
The Gunners, with 24 points from 19 matches, are 11th in the Premier League.
The third of the Big 3 London clubs, Chelsea, were unimpressive at Stamford Bridge against visiting Southampton, who started the day in the relegation zone.
Chelsea seemed flat in the wake of their most important victory of the season - last weekend's defeat of Spurs in the capital derby - and Southampton triumphed 2-0 on goals by Michael Obafemi, in the 31st minute, and Nathan Redmond (min. 73).
Despite losing three of their last four Premier League matches, Chelsea hang onto fourth place with 32 points, while Southampton vault to 14th.
While Arteta had to be content with a draw, Carlo Ancelotti started his stint as Everton manager with a 1-0 win against Burnley at Goodison Park.
But the Toffies had to work hard for the 3 points and Dominic Calvert-Lewin's winner came only in the 80th minute.
Everton moved up to 13th place with 22 points, two behind Burnley.
In a relegation battle, Aston Villa edged last-place Norwich City 1-0 on Conor Hourihane's goal to move up to 18th, just 1 point behind 17th-place West Ham United, 2-1 losers Thursday to Crystal Palace, who are 8th in the table with 26 points.
Watford, who sit one place from the bottom spot, earned a point with a 1-1 draw against sixth-place Sheffield United.
( With inputs from IANS )