Cody Gakpo, Darwin Nunez, and Mohamed Salah each scored twice, with Roberto Firmino also getting on the scoresheet in the 7-0 win at Anfield.
The result all but ended United's hopes of a first league title in a decade as they remain 14 points behind leaders Arsenal in third place. Liverpool, however, are closing in on a top-four finish and are now just three points behind fourth-placed Tottenham with a game in hand.
Jurgen Klopp's side has struggled this season after coming close to winning an unprecedented quadruple of trophies last year. But following a 5-2 loss to Real Madrid, they have been able to get back in the race for a place in next season's Champions League, winning 13 points from a possible 15 in the Premier League.
Manchester United manager, Erik ten Hag, encouraged his players to embrace the hostile environment of Anfield, where the visitors have not won since 2016.
Although United had better chances in the first half, Liverpool produced a moment of quality to break the deadlock just before half-time. Andy Robertson sliced open the United defence to set up Gakpo for the opener.
In the second half, Liverpool's new-look front three finally clicked as Nunez and Gakpo punished sloppy United defending.
Salah got the goal his performance deserved, crashing in Nunez's through ball off the underside of the bar. Salah then moved outright as Liverpool's all-time Premier League goalscorer with 129 with a simple tap-in after more shambolic United defending.
Firmino, who was revealed to be leaving the club at the end of the season, came off the bench to complete the rout with a remarkable seventh goal two minutes from time.