Manchester United dominated the game to achieve the victory that pushed coach Erik ten Hag's side towards sixth place in the table with 27 points after 15 games, while Chelsea's balance is frozen at 19 points in tenth place.
Man United's win comes at a difficult time for beleaguered Ten Hag, who has recently been haunted by media reports of problems inside the dressing room.
The "Reds" beat Sheffield United at the bottom of the standings with two clean goals. Dutch defender Virgil van Dijk (37) and Poland's Dominik Soboszlai (90+4) scored Liverpool's goals.
The sons of Jürgen Klopp raised their tally to 34 points in second place, two points behind leaders Arsenal, winner with difficulty over Luton Town 4-3, Tuesday, in the opening of the 15th stage, and moved away by two points from Aston Villa third and four points from Manchester City fourth.