The Reds were in complete control throughout the 90 minutes and took the lead through Roberto Firmino's far post header. They doubled that advantage in the second half as substitute James Milner netted from the penalty spot following a handball by Caglar Soyuncu.
Two further goals in four minutes from Firmino and Trent Alexander-Arnold saw Liverpool rack up a comprehensive three points.
Story of the Match
Reds look ominous
Despite Leicester heading into the match only one place behind Jurgen Klopp's men, the gap on the pitch was vast straight from kick off. Alexander-Arnold tested Kasper Schmeichel with a powerful drive in the first minute before Sadio Mane somehow lifted over only yards from goal.
The tone was set from then on. Mo Salah wasted a great chance as he skipped around Schmeichel, only to find the side-netting. Firmino was not going to miss though as he was left unmarked at the back post to nod the ball low into the net for the opener.
Mane could have doubled the lead only minutes later as he bustled through the Leicester defence but Schmeichel this time produced a great save to deny the forward.
Sucker punch for Rodgers' men
Just as the hosts built up some momentum after the break, Liverpool then silenced the King Power Stadium again as they doubled the lead. Soyuncu was adjudged to have handled in the area from a corner, giving substitute Milner the opportunity to score his second penalty against the Foxes this season. He did just that as he calmly stroked home from the penalty spot.
Alexander-Arnold then had another say only minutes later as he rounded off a flowing move to put in a perfect low ball to Firmino, with the Brazilian powering the ball into the top corner with a clinical finish.
The 21-year-old's evening was not finished there though as he picked up space on the right and thundered the ball into the bottom corner of the Leicester net to round off a perfect evening for the table-topping Reds.
TAA the best right-back in Europe?
This really was a brilliant showing from Liverpool defender Trent Alexander-Arnold. Two assists and a goal of his own really do not tell the full story of his evening. A constant menace to the Leicester backline with his delivery, the youngster was also assured in defence. He really does look the real deal.
Reality check for Leicester
Despite sitting second, Leicester's season has now taken two significant blows having lost to Manchester City and Liverpool. Brendan Rodgers' men were second best throughout the entirety of the game and whilst they have earned the plaudits they have received this season, this should give them plenty of reason to refocus ahead of a hectic January.
Title wrapped up at Christmas?
Surely Liverpool will be lifting the Premier League crown come May. Now 13 points clear at the top of the table, it looks highly unlikely anyone is going to challenge the irrepressible Reds and should they turn in more showings like Thursday's at the King Power Stadium, that will most definitely be the case.