Liverpool moved to 76 points from 32 games with title rivals Manchester City on 74 points from one game fewer, with Pep Guardiola's side hosting Brighton and Hove Albion at the Etihad tomorrow.
It was a miserable night for United who are now without a win in their last eight league clashes with Liverpool and who have failed to score in five of their last six trips to Anfield.
United dropped below Arsenal on goal difference, falling to sixth place on 54 points, having played two games more than the Gunners.
Tottenham Hotspur currently occupy fourth spot on 57 points but even though United remain in with a chance of qualifying for the Champions League there was nothing in their performance that indicated they merited such a reward.
Interim manager Ralf Rangnick, who was without Cristiano Ronaldo, mourning the death of his newborn son, opted to play five at the back with Phil Jones drafted in.
It was an approach that simply did not work and Rangnick abandoned it at halftime but by then Liverpool were 2-0 up and in control.
Colombian Luis Diaz gave Liverpool a fifth-minute lead, tapping in from close range after Sadio Mane set Mohamed Salah free down the right and the Egyptian delivered a pinpoint low cross for a simple finish.
United's problems got worse in the 10th minute when Paul Pogba limped off injured and with Rangnick's side struggling to get any foothold in the game, it was no surprise when the home side doubled their advantage.
Mane again provided the spark with a superb first-time pass finding Salah who, having lost his bewildered marker Diogo Dalot, cut in from the right and provided his trademark left-foot finish. The Senegalese creator turned finisher in the 68th minute, making it 3-0 after Andy Robertson broke down the left and then Diaz picked out Mane whose first time finish on the turn flew into the bottom corner.
Salah completed the rout in the 85th minute as substitute Diogo Jota threaded a pass through to the Egyptian, who beat David De Gea with a deflected finish that came off the leg of the sliding Aaron Wan-Bissaka.
The Anfield crowd revelled in the humiliation of their North West rivals while a section of the visiting fans chose to leave early.
Meanwhile Fulham achieved promotion back to the Premier League with a 3-0 home win over Preston North End which guaranteed the London side a top-two finish in the second-tier Championship.
League leaders Fulham -- who were relegated from the top flight last year -- now have 86 points from 42 games.
Promotion is worth up to $350 million, according to last year's Deloitte Annual Review of Football Finance.
The top two in the division are promoted to the Premier League while the teams that finish third to sixth go into the playoffs to fight for the final spot.
Only Nottingham Forest could have denied Fulham promotion but they are now 16 points behind the Londoners and can get a maximum of 15 more from their remaining five games.
Fulham's next challenge is to win the Championship title. They are nine points clear of second-placed Bournemouth, who have 77 points and a game in hand on the leaders.
Huddersfield Town are in third place on 73 ahead of Luton Town with 71, Forest on 70 and Sheffield United who currently occupy the final playoff place with 66 points.