Mohamed Salah and Sadio Mane struck twice, while Joel Matip and Virgil van Dijk were also on target as the Reds cut the gap on leaders Manchester City to just three points.
Jurgen Klopp's troops were in inspired form on the night. However, the Peacocks were also culpable for their shambolic defence that has now conceded 56 goals, the most in the English top flight this season.
The hosts were 3-0 by half-time, courtesy of two penalties from Salah either side of a goal from Matip, before Mane added a brace of his own late on. There was more misery to come for the visitors as Van Dijk also joined the act in the 93rd minute to make it six.
On that note, here are the player ratings for Liverpool:
Alisson - 6/10
The Liverpool custodian lost the ball to Daniel James early on in a near-disastrous moment for him, but aside from that, he wasn't called into action much.
Trent Alexander-Arnold - 7/10
He scampered upfield as usual, and laid some amazing crosses. He was unlucky not to bag an assist on a goal-crazy night for the Reds.
Joel Matip - 8/10
He cleared Alisson's mess early on after the ball fell kindly to him. Matip then doubled Liverpool's advantage at the other end with a nice finish.
Virgil van Dijk - 8/10
The Dutchman had a comfortable game defensively. He then put the final nail in Leeds' coffin with a stoppage-time goal. Van Dijk loves playing at Anfield. He has now equalled the record for most Premier League home games unbeaten (59) for a single club.
Andrew Robertson - 7.5/10
He was electric down the left flank, providing a vibrant attacking presence, with four key passes and an assist.
Curtis Jones - 8/10
Jones was unplayable on the night. Leeds had no answer to his precocious dribbling skills, and he made some excellent ball recoveries too.
Fabinho - 7.5/10
The Brazilian's intelligent positioning impeded Leeds' movement, and his distribution was top-notch too.
Thiago Alcantara - 7.5/10
Alcantara was at the top of his game, jumping into perfectly timed tackles and showcasing his staggering passing range.
Mohamed Salah - 9/10
The Egyptian ace was at it again, taking Leeds to the cleaners with his movement, speed and directness. Two excellent first-half penalties essentially ended the contest by half-time.
Salah now has the most goal contributions (160) by an African player in Premier League history. In the process, he downed the erstwhile record of Didier Drogba, having played a whopping 72 games less.
Sadio Mane - 9/10
Mane played through the middle on the night, and was an absolute menace for Leeds. He won a penalty, and scored two late goals to add gloss to the scoreline. He is now the only played with at least ten goals in each of the last eight Premier League campaigns.
Luis Diaz - 7/10
There were no goals for him on the night, but Diaz was integral to Liverpool's resounding win. His hold-up play and decisions in the final third were impressive.
Ratings of Liverpool substitutes against Leeds United
Jordan Henderson - 7.5/10
He bagged an assist for Mane's first goal by running into the right-inside channel and cutting it back for the Senegalese to fire home.
Divock Origi - 7/10
The Belgian fired a shot that Leeds keeper Illan Meslier parried into the path of Mane to tap home the Reds' fifth of the night.
James Milner - 6.5/10
Milner hammered a strike off a corner, but it was blocked by a wall of white shirts.
Where does Mane rank in Paul Merson's 5 greatest Liverpool signings of the Klopp era? Click here